help

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 Remember the form of a quadratic function equation: y = f(x) = ax2 + bx + c

2. You will use: W(x) = -0.1x2 + bx + c where (-0.1x2 + bx) represents the store’s variable costs and c is the store’s fixed costs.

3. Choose a value between 10 and 20 for b; that value does not have to be a whole number.

4. So, W(x) is the store’s total monthly costs based on the number of items sold, x.

5. Think about what the variable and fixed costs might be for your fictitious storefront business – and be creative. Start by choosing a fixed cost, c, between $5,000 and $10,000, according to the following class chart (make sure the combination of your b and your c do not match exactly any of your classmates’):

If your last name starts with the letter

Choose a fixed cost between

A–E

$5,000–$5,700

F–I

$5,800–$6,400

J–L

$6,500–$7,100

M–O

$7,200–$7,800

P–R

$7,800–$8,500

S–T

$8,600–$9,200

U–Z

$9,300–$10,000

6. Post your chosen c value in your subject line, so your classmates can easily scan the discussion thread and try to avoid duplicating your c value. (Different c values make for more discussion.)

7. Your monthly cost is then, W = -0.1x2 + bx + c.

8. Substitute the c value chosen in the previous step to complete your unique equation predicting your monthly costs.

9. Next, choose two values of x (number of items sold) between 50 and 100. Again, try to choose different values from classmates.

10. Plug these values into your model for W and evaluate the monthly business costs given that sales volume.

11. Discuss results of these cost calculations and how these calculations could influence business decisions.

12. Is there a maximum cost for your General Store? If so, how many units must be sold to produce the maximum cost, and what is that maximum cost? How would knowing the number of items sold that produces the maximum cost help you to run your General Store more efficiently?

Statistical Homework

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Statistical Homework
For questions 2 and 3 you will need the data analysis tools in Excel. please also give lament, simple explanation of how to solve problem.

 

In question 2 you will use the regression function from the data analysis tools. Carefully read the problem to figure out which is the dependent variable and which is the independent variable. In parts c, e, and f you are asked to interpret the meaning of different measures. This is where you can show your understanding.
In question 3 you will perform hypothesis testing on multiple populations. Be very careful with selecting the test statistic. Tackling question 3 as a series of pair wise comparisons is not the correct way to solve this problem. This will build an error and the actual significance level will be different from the desired one. 

1. The Connecticut Board of Education is concerned that first year female High school teachers are receiving lower salaries than their male counterparts. Two independent random samples have been selected 630 observations from population 1 (female high school teachers) and 610 from population 2 (male high school teachers). The sample means obtained are X1(bar)=$46 k and X2(bar)=$47 k. It is known from previous studies that the population variances are 4.1 and 5.0 respectively. Using a level of significance of .05, is there evidence that the first year female high school teachers are receiving lower salaries? Fully explain your answer. 

Simple Regression
2. A CEO of a large pharmaceutical company would like to determine if he should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling diabetes. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called DIB and the number of orders received. The manufacturing process of this drug is very difficult and requires stability so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new drug. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received. 
The use of linear regression is a critical tool for a manager’s decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. The results are as follows: 

Month Advertising Cost Number of Orders
1 $69,430.00 2,902,000
2 72,620 3,800,000
3 79,58 0 3,299,000
4 60,670 2,430,000
5 69,180 3,367,000
6 73,140 4,011,000
7 93,370 4,888,000
8 78,880 4,935,000
9 94,990 5,555,000
10 77,230 3,654,000
11 91,380 5,598,000
12 52,900 2,967,000
13 63,270 2,899,000
14 89,190 4,245,000
15 90,030 4,934,000
16 79,210 3,853,000
17 85,770 5,625,000
18 84,530 5,778,000
19 99,760 5,999,000
20 102,640 6,834,000
a. Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amount of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under Tools > Data Analysis. The Scatterplot can more easily be generated using the Chart procedure. 
NOTE: If you do not have the Data Analysis option under Tools you must install it. You need to go to Tools select Add-ins and then choose the 2 data toolpak options. It should take about a minute.
b. Assuming there is a statistically significant relationship, use the least squares method to find the regression equation to predict the advertising costs based on the number of orders received. Please use the regression procedure within Excel under Tools > Data Analysis to construct this equation. 
c. Interpret the meaning of the slope, b1, in the regression equation. 
d. Predict the monthly advertising cost when the number of orders is 5,100,000. (Hint: Be very careful with assigning the dependent variable for this problem) 
e. Compute the coefficient of determination, r2, and interpret its meaning. 
f. Compute the standard error of estimate, and interpret its meaning. 

Hypothesis Testing on Multiple Populations 
3. The Course Manager for AMBA 610 wants to use a new tutorial to teach the students about business ethics. As an experiment she randomly selected 18 students and randomly assigned them to one of three groups which include either a PowerPoint presentation created by the faculty, AuthorGen Presentation created by the faculty, or a well known tutorial by the ABC company. After completing their assigned tutorial, the students are given a Business Ethics test. At the .01 significance level, can she conclude that there is a difference between how well the different tutorials work for the students?
Students Grades on the Business Ethics Test following the Tutorial

PowerPoint Tutorial AuthorGen Tutorial ABC Tutorial
98 79 66
94 76 78
91 75 79
88 83 96
98

Statistics

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Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings of the 11 employees both before the new diet and one month after use of the diet began. At 5% level of significance, test the claim that the new diet is effective in lowering cholesterol. Assume differences in cholesterol readings are normally distributed in the population.

 

Employee             Before                       After

1                             255                            197

2                             230                             225

3                             290                             215

4                             242                             215

5                             300                             240

6                              250                            235

7                             215                             190

8                              230                             240

9                              225                             200

10                            219                             203

11                            236                              223 

 

 

EXPECTATIONS
– Draw graphs and charts when appropriate and necessary to demonstrate your reasoning! Label all graphs and charts!
– Display formulas. Write complete sentences to summarize your conclusions.
– If use any table values, clearly state which tables you used (e.g. Table A-2, etc.).
-Attach excel output when appropriate or necessary (e.g. a scatterplot, etc.)

HYPOTHESIS TESTING QUESTIONS
Your work for all statistical hypothesis testing questions should include the following:
1. Established Ho and Ha.
2. Summary statistics (either computed or given in the problem)
3. The name of the test (e.g. 2sampleTtest or T-test about correlation, etc.)
4. A formula to compute a test statistic (e.g. 1Prop-Z test statistic, etc.)
5. A p-value of the test and/or a critical value from a statistical table.
6. Clearly state the decision rule you use the reach a conclusion. (You may have to sketch a graph to show rejection regions.) Do you “Reject Ho” or do you “Fail to Reject Ho”?
7. State your conclusion in plain language. Use complete sentences.

 

 

 

 

 

Multi Choice Problems…

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Question 1 of 20
 0.0/ 5.0 Points
Write the vector v in terms of i and j whose magnitude and direction angle θ are given.

= 8, θ = 30°
A. v = -4i + 4j  
B. v = 4i + 4j  
C. v = 4i + 4j  
D. v = 4i + 4j  

Question 2 of 20
 0.0/ 5.0 Points
Select the representation that does not change the location of the given point. (4, 110°)
A. (4, 470)°  
B. (4, 290)°  
C. (-4, 200)°  
D. (-4, 470)°  

Question 3 of 20
 0.0/ 5.0 Points
Find the quotient of the complex numbers. Leave answer in polar form.

z1 =

z2 =

A.  
B.  
C.  
D.  

Question 4 of 20
 0.0/ 5.0 Points
Find the unit vector that has the same direction as the vector v. v = 3i + j
A. u = i + j  
B. u = i + j  
C. u = 3i + j  
D. u = i + j  

Question 5 of 20
 5.0/ 5.0 Points
Polar coordinates of a point are given. Find the rectangular coordinates of the point.
A. (-1.6, -1.3)  
B. (1.6, 1.3)  
C. (1.3, 1.6)  
D. (-1.3, -1.6)  

Question 6 of 20
 0.0/ 5.0 Points
Find the work done by a force of 4 pounds acting in the direction of 41° to the horizontal in moving an object 5 feet from (0, 0) to (5, 0).
A. 13.1 ft-lb  
B. 16.2 ft-lb  
C. 15.1 ft-lb  
D. 30.2 ft-lb  

Question 7 of 20
 0.0/ 5.0 Points
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 6, c = 11, B = 109°
A. b = 14.1, A = 24°, C = 47°  
B. b = 19.9, A = 22°, C = 49°  
C. b = 17, A = 26°, C = 45°  
D. no triangle  

Question 8 of 20
 0.0/ 5.0 Points
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 15° C = 113° b = 49
A. A = 50°, a = 176.3, c = 151.2  
B. A = 52°, a = 149.2, c = 174.3  
C. A = 52°, a = 151.2, c = 176.3  
D. A = 50°, a = 174.3, c = 149.2  

Question 9 of 20
 0.0/ 5.0 Points
Find all the complex roots. Write the answer in the indicated form. The complex cube roots of 27(cos 234° + i sin 234°) (polar form)
A. -3(cos 78° + i sin 78°), 3(cos 198° + i sin 198°), -3(cos 318° + i sin 318°)  
B. 3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), 3(cos 158° + i sin 158°)  
C. -3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), -3(cos 158° + i sin 158°)  
D. 3(cos 78° + i sin 78°), 3(cos198° + i sin 198°), 3(cos 318° + i sin 318°)  

Question 10 of 20
 5.0/ 5.0 Points
Find the specified vector or scalar.

u = -4i + 1j and v = 4i + 1j; Find .
A.  
B. 8  
C. 5  
D. 2  

Question 11 of 20
 5.0/ 5.0 Points
Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = j, w = 4i
A. orthogonal  
B. parallel  
C. neither  

Question 12 of 20
 0.0/ 5.0 Points
Write the complex number in polar form. Express the argument in degrees. 4i
A. 4(cos 0° + i sin 0°)  
B. 4(cos 270° + i sin 270°)  
C. 4(cos 90° + i sin 90°)  
D. 4(cos 180° + i sin 180°)  

Question 13 of 20
 0.0/ 5.0 Points
The wind is blowing at 10 knots. Sailboat racers look for a sailing angle to the 10-knot wind that produces maximum sailing speed. This situation is now represented by the polar graph in the figure shown below. Each point (r, θ) on the graph gives the sailing speed, r, in knots, at an angle θ to the 10-knot wind. What is the speed to the nearest knot, of the sailboat sailing at 120° angle to the wind?
A. 8 knots  
B. 9 knots  
C. 7 knots  
D. 10 knots  

Question 14 of 20
 0.0/ 5.0 Points
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 7, b = 7, c = 5
A. A = 70°, B = 70°, C = 40°  
B. A = 69°, B = 69°, C = 42°  
C. A = 42°, B = 69°, C = 69°  
D. A = 69°, B = 42°, C = 69°  

Question 15 of 20
 0.0/ 5.0 Points
Plot the complex number. 2 + i
A.  
B.  
C.  
D.  

Question 16 of 20
 0.0/ 5.0 Points
Find the magnitude and direction angle θ, to the nearest tenth of a degree, for the given vector v. v = -4i – 3j
A. 5; 233.1°  
B. 7; 216.9°  
C. 5; 216.9°  
D. 5; 36.9°  

Question 17 of 20
 0.0/ 5.0 Points
Find the quotient of the complex numbers. Leave answer in polar form.

z1 = 
z2 =

A.  
B.  
C.  
D.  

Question 18 of 20
 0.0/ 5.0 Points
Graph the polar equation.

r = 2 + 2sin θ
A.  
B.  
C.  
D.  

Question 19 of 20
 0.0/ 5.0 Points
Polar coordinates of a point are given. Find the rectangular coordinates of the point. (-5, -180°)
A. (-5, 0)  
B. (0, -5)  
C. (0, 5)  
D. (5, 0)  

Question 20 of 20
 0.0/ 5.0 Points
Plot the complex number.

-5– 5i
A.  
B.  
C.  
D.  

THIS MUST BE DONE RIGHT IF YOU CAN NOT FO THE WORK FOR MY PRICE DO NOT ASK TO HELP. I WILL DISPUTE IF I AM BEING DONE WRONGLY AND WILL ASK FOR REFUND THROUGH PAYPAL. MATH GENIUS ONLY

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Assignment 1: Discussion—The Traveling Salesman Problem

 

Some problems in mathematics can be stated very simply but may involve complex solutions. One of the most famous of these is the Traveling Salesman Problem or, as it is known to mathematicians, the TSP.

 

The TSP is the problem of deciding the most efficient route to take between multiple cities to save time and money. This problem occupies the minds of managers from shipping companies to postal services to airlines. The routes you choose affect both your income and your expenses. Therefore, the TSP is an extremely important problem in the modern world. If you haven’t already done so, please read the section of your textbook which provides a detailed overview of the TSP and the numerous methods used to find solutions.

 

Now, put yourself in the role of a business manager that must make deliveries to five different cities in five different states. You may pick the five cities that you would like to use in this scenario. Prepare a multiple paragraph response of between 200-300 words addressing the following:

 

  • State the problem you are solving making sure to mention the five delivery destinations.
  • Clearly demonstrate each step you followed to reach the most efficient route between these five cities.
  • Consider all of the expenses that may be incurred while making these deliveries and how choosing an efficient route helps to curtail these costs.

 

Respond to at least two posts contributed by your peers and comment on the problem they demonstrated and the steps they employed to reach a solution. What would you have done the same or different? Do you agree with the solution? Can you suggest a different approach to solving the same problem?

By Saturday, March 8, 2014, deliver your assignment to the appropriate Discussion Area. Through Wednesday, March 12, 2014, review and comment on your peers’

STAT200 : Introduction to Statistics Final Examination, Fall 2013

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STAT 200 practice exam

 

Refer to the following frequency distribution for Questions 1, 2, 3, and 4.

 

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 PM and 4:00 PM on a Friday afternoon.

 

Checkout Time (in minutes)

Frequency

1.0 – 1.9

5

2.0 – 2.9

3

3.0 – 3.9

7

4.0 – 4.9

3

5.0 – 5.9

2

 

 

1.       What percentage of the checkout times was less than 4 minutes? (5 pts)

 

 

__________

 

2.       Calculate the mean of this frequency distribution. (10 pts)

 

__________

 

3.       In what class interval must the median lie? (You don’t have to find the median) (5 pts)

 

 

__________

 

 4.    Assume that the smallest observation in this dataset is 1.2 minutes.  Suppose this observation were

        incorrectly recorded as .2 instead of 1.2 minutes. (5 pts)

 

        Will the mean increase, decrease, or remain the same?

 

                                                                                                                                                                                ___________

 

        Will the median increase, decrease or remain the same?

 

                                                                                                                                                                                ____________

 

 

 

Refer to the following information for Questions 5 and 6

 

A 6-faced die is rolled two times.  Let A be the event that the outcome of the first roll is even.   Let B be the event that the outcome of the second roll is greater than 4.

 

 

5.    What is the probability that the outcomes of the second roll is greater than 4, given that the

       first roll is an even number? (10 pts)

 

 

                                                                                                                                                                                ____________

 

6.    Are A and B independent? (5 pts)

 

                                                                                                                                                                                ____________

 

 

Refer to the following data to answer questions 7 and 8.

 

A random sample of Stat 200 weekly study times in hours is as follows:

 

4,   14,   15,   17,   20

 

7.     Find the standard deviation. (10 pts)

 

 

                                                                                                                                                                             _____________

 

 

8.    Are any of these study times considered unusual in the sense of our textbook? (2.5  pts)

 

                                                                                                                                                                                _____________

 

      Does this differ with your intuition? (2.5 pts)

 

 

                                                                                                                                                                                _____________

Refer to the following situation for Questions 9, 10, and 11.

 

The five-number summary below shows the grade distribution of two STAT 200 quizzes.

 

 

Minimum

Q1

Median

Q3

Maximum

Quiz 1

12

40

60

95

100

Quiz 2

20

35

50

90

100

 

 

For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. (5 pts each)

 

9.    Which quiz has less interquartile range in grade distribution?

 

                                                                                                                                                                                _____________

 

 

10.   Which quiz has the greater percentage of students with grades 90 and over?

 

                                                                                                                                                                                _____________

 

 

11.   Which quiz has a greater percentage of students with grades less than 60?

 

 

                                                                                                                                                                                ____________

 

 

 

Refer to the following information for Questions 12 and 13.

 

There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only:  AP Calculus and AP Statistics.  The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people.  There are 43 overachieving seniors on both rosters.

 

12.    What is the probability that a randomly selected senior is in at least one of the two classes?

(10 pts)

 

 

                                                                                                                                                                                ____________

 

 

13.    If the student is in the Calculus class, what is the probability the student is also in the Statistics

          class? (10 pts)

 

                                                                                                                                                                                _____________

 

14.    A random sample of 225 SAT scores has a mean of 1500. Assume that SAT scores have a population

         standard deviation of 300.  Construct a 95% confidence interval estimate of the mean SAT scores.

        (15 pts)

 

                The proper distribution for calculating the Confidence Interval is:

                                                                                               

                                                                                                                Chi Square,         t distribution,     z distribution

 

                The lower and upper limits for the 95% confidence interval are:

 

 

 

                                                                                                                                ___________                   ___________  

 

Refer to the following information for Questions 15, 16, and 17.

 

A box contains 5 chips.  The chips are numbered 1 through 5.  Otherwise, the chips are identical.  From this box, we draw one chip at random, and record its value.  We then put the chip back in the box.  We repeat this process two more times, making three draws in all from this box.

 

15.    How many elements are in the sample space of this experiment? (5 pts)

 

 

                                                                                                                                                                                _____________

 

16.  What is the probability that the three numbers drawn are all different? (10 pts)

 

 

                                                                                                                                                                                _____________

 

17.   What is the probability that the three numbers drawn are all odd numbers? (10 pts)

 

 

                                                                                                                                                                                _____________

 Questions 18 and 19 involve the random variable x with probability distribution given below.

 

X

2

3

4

5

6

P(x)

0.1

0.2

0.4

0.1

0.2

                                   

 

18.    Determine the expected value of x. (10 pts)

 

 

 

 

                                                                                                                                                                                _____________

 

19.   Determine the standard deviation of x. (10 pts)

 

 

 

 

                                                                                                                                                                                _____________

 

 

Consider the following situation for Questions 20 and 21.

 

Mimi just started her tennis class three weeks ago.  On Average, she is able to return 15% of her opponent’s serves.  If her opponent serves 10 times, please answer the following questions.

 

20.   Find the probability that she returns at most 2 of the 10 serves from her opponent. (10 pts)

 

 

                                                                                                                                                                                                                                                                                                                                                                                             _____________            

 

21.    How many seves is she expected to return? (5 pts)

 

 

                                                                                                                                                                                _____________

 


 

22. Given a sample size of 64, with sample mean 730 and sample standard deviation 80, we perform

       the following hypothesis test. (20 pts)

 

       Ho   μ= 750

       H1   μ < 750

 

What is the appropriate distribution for performing this Hypothesis test?

 

Z distribution,             t distribution,                  Chi Square distribution,             Empirical Rule

 

What is the critical value of the test statistic at α= 0.05 level?

 

                                                                                                                                                                                ____________

                Calculate the test statistic.

 

 

                                                                                                                                                                                ____________

 

What is the P-value for this Hypothesis Test?

 

                                                                                                                                                                _____________

 

What is your conclusion (decision) for this hypothesis test at α= 0.05 level?  

 

                                                                                                                Null Hypothesis                               Alternate Hypothesis

 

 

Refer to the following information for Questions 23, 24, and 25.

 

The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.

 

23.    What is the probability that a randomly selected pecan tree is between 10 and 12 feet tall? (10 pts)

 

 

 

                                                                                                                                                                                _____________

24.    Find the 3rd quartile of the pecan tree distribution. (5 pts)

 

 

                                                                                                                                                                                _____________

 

25.    If a random sample of 100 pecan trees is selected, what is the standard deviation of the sample mean?  (5 pts)

 

                                                                                                                                                                                _____________

26.          Consider the hypothesis test given by

 

Ho   μ   =   530

H1   μ   ≠   530

 

In a random sample of 81 subjects, the sample mean is found to be 524.  Also, the population standard deviation is σ= 27. (20 pts)

 

Calculate the Test Statistic.

 

 

 

 

                                                                                                                                                                ____________

 

What is the P-value for this test?

 

 

 

 

                                                                                                                                                                ____________

 

 

 

Is there sufficient evidence to justify the rejection of Ho at α= 0.01 level?

 

 

 

Do not reject the Null Hypothesis

 

Accept the Alternate Hypothesis

 

                                There is insufficient evidence to make a decision

 


 

 

27.    A certain researcher thinks that the proportion of women who say that the earth is getting warmer

          is greater than the proportion of men. (25 pts)

 

          In a random sample of 250 women, 70% said that the earth is getting warmer.

          In a random sample of 220 men, 68.18% said that the earth is getting warmer.

 

          At the .05 significance level, is there sufficient evidence to support the claim that the proportion of

          women saying the earth is getting warmer is higher than the proportion of men saying the earth is

          getting warmer?

 

What is the Null Hypothesis?

 

 

                                                                                                                                                _____________

What is the Alternate Hypothesis?

 

 

                                                                                                                                                _____________

 

                                                                                                                               

What is the numerical value of z critical?

 

                                                                                                                                                _____________

 

What is the numerical value of the test statistic?

 

 

 

 

                                                                                                                                                _____________

 

What is the P-value for this Hypothesis test?

 

                                                                                                                                                _____________

 

What is your decision based upon this Hypothesis test?

 

                                                                                                                                                _____________

 

 

 

Refer to the following data for Questions 28 and 29.

 

X

0

– 1

1

2

3

Y

4

– 2

5

6

8

                           

 

28.    Find an equation of the least squares regression line. (15 pts)

 

 

 

 

 

What is the Y intercept of the equation?

 

                                                                                                                                                _____________

 

What is the slope of the equation?

 

                                                                                                                                                _____________

 

 

 

                                                                                                                                   Y = ______  + ______x

 

Answer the following questions to receive full credit for this problem.

 

 

∑x =  _______,                                 ∑y =   _______,                                ∑x2 =  _______,                                ∑xy =   _______

 

 

29           Using the equation you calculated in question 28 What is the predicted value of y if x=4? (10 pts)

 

 

 

                                                                                                                                                                                ___________


 

30.    The UMUC Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20%          yellow, 20% orange, 10% green, and 10% tan.  Each piece of candy in a random sample of 100 plain          M&M’s was classified according to color, and the results are listed below.  Use a 0.05 significance          level to test the claim that the published color distribution is correct. (25 pts)

 

Color

Brown

Yellow

Orange

Green

Tan

Number

45

13

17

7

18

 

 

What is the Null Hypothesis?

 

                                                                                                                                                __________________

 

What is the Alternate Hypothesis?

 

 

                                                                                                                                                __________________

 

What is the degrees of freedom for this Hypothesis test?

 

                                                                                                                                                __________________

 

What is the numerical Chi Square critical value?

 

                                                                                                                                                __________________

 

What is the numerical value of the Chi Square test statistic?

 

 

                                                                                                                                                __________________

 

 

 

Having completed the Hypothesis test what is the appropriate decision?

 

 

                                                                                                Null Hypothesis                                Alternate Hypothesis                    

 

 

 

31.          Please note:  Each time you re-due the Final Exam the answer to question 31 may change, but the subject matter and format will not change.

 

                Example question:

 

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. (1 pt)

 

                A woman experienced a tax audit.  The tax department claimed that the woman was audited because she was randomly selected from all taxpayers.

 

                What type of sampling did the tax department use?

 

32.          Problem 32 is the Honor Pledge.  This question must be answered (truthfully) in the positive in order to receive credit for taking the Final Exam.

 

                                                            

 

probability and measures of variations.

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Quiz 2

Part 1. Descriptive Statistics. Measure of Variation.

Question 1

The two boxplots show the weights of the male and female students in a class.

Which of the following is NOT correct?

a. About 50% of the male students have weights between 150 and 183 lbs.

b. About 25% of female students have weights more than 128 lbs.

c. The median weight of male students is about 162 lbs.

d. The mean weight of female students is about 112.

e. The male students have more variability than the female students.

Question 2

A set of scores from a vocabulary test given to a large group of international students can be summarized with this five number summary: {20, 35, 45, 50, 60} Determine which of the following statements about the distribution CANNOT be

justified:

a. About 75% of the scores are equal to or above 35.

b. There are more scores from 35 to 45 than scores from 45 to 50.

c. The interquartile range is 15.

d. The distribution is skewed to the left or low end.

e. The range is 40

Question 3

Two sections took the same vocabulary quiz. Use the 5-number summary {20,30,35,45,60} to construct a boxplot for

Section I and use the summary {20,35,45,50,60} to construct a boxplot for Section II. Use the same scales for both plots,

of course. Based on the two boxplots, which of the following statements about the two sections CANNOT be justifies?

a. The median of Section II is greater than the median for Section I.

b. About 75% of the scores in Section II are greater than the or equal to about 50% of the scores in Section I.

c. There are the same number of scores in Section I and Section II.

d. The range of scores for Section I is equal to the range of scores for Section II.

e. The interquartile ranges are equal for both sections.

Question 4

Sam determined how much students spend per week on reading materials. He constructed separate graphs for those

who live on campus and those who live off campus.

Sam concluded that students who live off campus have different spending habits from those who live on cam pus.

a. Agree. Students who live off campus probably work and have more spending money.

b. Disagree. The medians are nearly equal.

c. Agree. There is more variability in costs for off-campus students than for on-campus students.

d. Disagree. The ranges are the same.

Question 5

Suppose that you measure the height of college woman and calculate a mean of 66 inches with standard deviation of

2.5 inches. Then you notice that the end of the measuring tape is badly worn and each woman’s height is one inch too

high. If you revise the measures by subtracting one inch from each value, determine the new mean and standard

deviation.

a. 66 inches and 2.5 inches.

d. 67 inches and 3.5 inches.

b. 66 inches and 1.5 inches.

e. 65 inches and 1.5 inch

c. 65 inches and 2.5 inches.

Question 6

In a study of heights of koala bears, scientists found that the distribution was strongly skewed left. However, in a study of

heights of polar bears, scientists found that the distrib ution was symmetric.

What measure of centre should the scientists use to describe their data?

a. Nothing. Bears are scary.

b. The koalas should be described with the median and interquartile range, and the polar bears with the mean and standard

deviation.

c. The koalas should be described with the mean and standard deviation, and the polar bears with the median and

interquartile range.

Question 7

Given the following data set: 3 5 6 7 7 8 8 8 9 9 9 10 102

Researcher detected the technical error in the last observation and replaced 102 by 10.2. What happens to Interquartile

Range (IQR) and Standard Deviation (SD)?

a. Both IQR and SD will increase.

b. The absolute value of IQR will change but the absolute value of SD will stay the same.

c. SD will decrease and IQR will not change.

d. Both IQR and SD will decrease.

Question 8

Which of the following sets of data has the largest standard deviation?

Set A: 57, 60, 60, 60, 60, 60, 60, 63

Set B: 57, 58, 59, 60, 61, 62, 63, 64

a. There is no way to tell without using a calculator.

b. Set A

c. Set B

Question 9

Two researchers collected the information about student’s monthly spending on rental DVD in two different campuses.

Researcher A: sample size n =125, Mean = $30, Standard Deviation = $5

Researcher B: sample size n =165, Mean = $15, Standard Deviation = $5

Select the best answer.

a. The variation of the data is not comparable because the sample size is different.

b. The variation of the data for researchers A and B is not comparable because the first mean is twice as large.

c. We cannot compare the variation because in calculating the standard deviations one researcher could have divided by (n)

and the other by (n-1)

e. The variation of data is similar for researchers A and B.

Question 10

Suppose a population generally has a symmetrical distribution with one of the measurements on this curve falls more than 3

standard deviations above the mean. What would you call this value?

a. An error. All the values should lie within 3 standard deviations of the mean.

b. A value that has a 99.7% chance of occurring, because of the Empirical Rule.

c. An extreme outlier.

d. None of the given answers.

Question 11

Shrek lives on a swamp. The condition of his swamp is very important to him so he regularly checks the temperature. Over

the course of the year he records the temperatures of his swamp. The median is 70 degrees, the first and third quartiles are

60 and 80 degrees respectively. The min and max temperatures were 26 and 115 degrees respectively. Were some

temperatures outliers?

a. Yes. There is at least one outlier and it is below the median

b. There are outliers both above and below the median

c. There are no outliers

d. Yes there is at least one outlier and it is above the median.

Question 12

A group of Statistics students took a 25-item multiple-choice test. Each question had four answers, only one of which was

correct. The correct answer was given a score of “1” and the wrong answers were given a score of “0”. The mea n and

standard deviation were computed, and the standard deviation was 0.

What we know about this distribution? Select the best answer.

a. The test was so hard that everyone missed all of the questions

b. About half of the scores were above the mean

c. Everyone correctly answered the same number of items

d. A calculation error must have been made in determining the standard deviation

Question 13

The amount of television viewed by today’s youth is of primary concern to Parents Against Watching Television ( PAWT). 300

parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched

television. The distribution of the data showed a bell-curved shape with the mean of 16 hours and the standard deviation of

4 hours.

Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the

distribution.

a. between 8 and 24 hours per week

b. between 4 and 28 hours per week

c. between 12 and 20 hours per week

d. less than 12 and more than 20 hours per week

Question 14

Assuming that resting systolic blood pressure for healthy woman under the age of 35 has a mean of 120 and a standard

deviation of 9. Also assuming that the distribution of these woman’s systolic blood pressures is unimodal and symmetric.

According to the Empirical Rule, about 16% of healthy woman of this age

a. have resting systolic blood pressure below 102.

b. have resting systolic blood pressure above 129.

c. have resting systolic blood pressure between 102 and 111.

d. have resting systolic blood pressure above 138.

Question 15

A town’s average snowfall is 49 inches per year with a standard deviation of 5 inches. The distribution is symmetric and bell

shaped. What amount of snowfall would you expect to be unusual for this town?

a. 53 inches

b. 63 inches

c. 35 inches

d. none of the given answers

Multi Choice Problems…

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Question 1 of 20
 0.0/ 5.0 Points
The finite sequence whose general term is an = 0.17n2 – 1.02n + 6.67 where n = 1, 2, 3, …, 9 models the total operating costs, in millions of dollars, for a company from 1991 through 1999.

Find

A. $21.58 million  
B. $27.4 million  
C. $23.28 million  
D. $29.1 million  

Question 2 of 20
 5.0/ 5.0 Points
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 8 terms of the geometric sequence: -8, -16, -32, -64, -128, . . . .
A. -2003  
B. -2040  
C. -2060  
D. -2038  

Question 3 of 20
 5.0/ 5.0 Points
Find the probability. What is the probability that a card drawn from a deck of 52 cards is not a 10?
A. 12/13  
B. 9/10  
C. 1/13  
D. 1/10  

Question 4 of 20
 0.0/ 5.0 Points
Find the common difference for the arithmetic sequence. 6, 11, 16, 21, . . .
A. -15  
B. -5  
C. 5  
D. 15  

Question 5 of 20
 0.0/ 5.0 Points
Find the indicated sum.
A. 28  
B. 16  
C. 70  
D. 54  

Question 6 of 20
 0.0/ 5.0 Points
Evaluate the expression.

1 –

A.  
B.  
C.  
D.  

Question 7 of 20
 0.0/ 5.0 Points
Find the sum of the infinite geometric series, if it exists. 4 – 1 + – + . . .
A. – 1  
B. 3  
C.  
D. does not exist  

Question 8 of 20
 0.0/ 5.0 Points
Find the probability. One digit from the number 3,151,221 is written on each of seven cards. What is the probability of drawing a card that shows 3, 1, or 5?
A. 5/7  
B. 2/7  
C. 4/7  
D. 3/7  

Question 9 of 20
 0.0/ 5.0 Points
A game spinner has regions that are numbered 1 through 9. If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 6?
A. 1/18  
B. 1/81  
C. 1/9  
D. 2/3  

Question 10 of 20
 5.0/ 5.0 Points
Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first four terms of the geometric sequence: 2, 10, 50, . . . .
A. 312  
B. 62  
C. 156  
D. 19  

Question 11 of 20
 0.0/ 5.0 Points
Write a formula for the general term (the nth term) of the geometric sequence.

, – , , –, . . .
A. an = n – 1  
B. an = –  (n – 1)  
C. an = n – 1
  
D. an = n – 1  

Question 12 of 20
 5.0/ 5.0 Points
Does the problem involve permutations or combinations? Do not solve. In a student government election, 7 seniors, 2 juniors, and 3 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done?
A. permutations  
B. combinations  

Question 13 of 20
 5.0/ 5.0 Points
Solve the problem. Round to the nearest hundredth of a percent if needed. During clinical trials of a new drug intended to reduce the risk of heart attack, the following data indicate the occurrence of adverse reactions among 1100 adult male trial members. What is the probability that an adult male using the drug will experience nausea?
A. 2.02%  
B. 1.73%  
C. 27.59%  
D. 2.18%  

Question 14 of 20
 0.0/ 5.0 Points
The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. an= 4n – 2
A. arithmetic, d = -2  
B. geometric, r = 4  
C. arithmetic, d = 4  
D. neither  

Question 15 of 20
 5.0/ 5.0 Points
Evaluate the factorial expression.
A. n + 4!  
B. 4!  
C. (n + 3)!  
D. 1  

Question 16 of 20
 5.0/ 5.0 Points
If the given sequence is a geometric sequence, find the common ratio.

, , , ,

A.  
B. 30  
C.  
D. 4  

Question 17 of 20
 5.0/ 5.0 Points
Solve the problem. Round to the nearest dollar if needed. Looking ahead to retirement, you sign up for automatic savings in a fixed-income 401K plan that pays 5% per year compounded annually. You plan to invest $3500 at the end of each year for the next 15 years. How much will your account have in it at the end of 15 years?
A. $77,295  
B. $75,525  
C. $76,823  
D. $73,982  

Question 18 of 20
 0.0/ 5.0 Points
Find the term indicated in the expansion.

(x – 3y)11; 8th term
A. -721,710x7y4  
B. -721,710x4y7  
C. 240,570x7y4  
D. 240,570x4y8  

Question 19 of 20
 0.0/ 5.0 Points
Find the probability. Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?
A. 1/12  
B. 5/18  
C. 3  
D. 1/18  

Question 20 of 20
 5.0/ 5.0 Points
Does the problem involve permutations or combinations? Do not solve. A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 15 members and any member can be elected to each position? No person can hold more than one office.
A. permutations  
B. combinations  

Since the population is always larger than the sample, the population mean is always smaller than or equal to the sample mean

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Question 1 of 25 1.0 Points

Since the population is always larger than the sample, the population mean:
A. is always smaller than or equal to the sample mean
B. is always larger than or equal to the sample mean
C. can be smaller than, or larger than, or equal to the sample mean
D. is always strictly less than the sample mean

Question 2 of 25 1.0 Points

What is the probability of drawing two queens in a row from a standard deck of cards without replacement?
A. 0.0045
B. 0.0059
C. 0.0015
D. 0.0385

Question 3 of 25 1.0 Points

If one tosses a coin enough times, the proportion of “heads” will approach 0.5. This is an example of:
A. the Law of Large Numbers
B. subjective probabilities
C. the Empirical Rule
D. the Central Limit Theorem

Question 4 of 25 1.0 Points

Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.

What is the probability that fewer than 40 batteries will last at least 8 hours?
A. 0.7986
B. 0.0789
C. 0.9598
D. 0.9211

Question 5 of 25 1.0 Points
Which term is NOT synonymous with the expected value of a discrete probability distribution?
A. μ
B. mean
C. theoretical average
D. variance

Question 6 of 25 1.0 Points

A discrete probability distribution:
A. lists all of the possible values of the random variable and their corresponding probabilities
B. can be estimated from long-run proportions
C. is a tool that can be used to incorporate uncertainty into models
D. is the distribution of multiple random variables

Question 7 of 25 1.0 Points
The normal distribution is:
A. a discrete distribution
B. the single most important distribution in statistics
C. a binomial distribution with only one parameter
D. a density function of a discrete random variable

Question 8 of 25 1.0 Points

The mean of a probability distribution can be:
A. a positive number
B. a negative number
C. zero
D. all of the above

Question 9 of 25 1.0 Points
The standard normal distribution has a mean of ___ and standard deviation of ___, respectively.
A. 0 and 1
B. 1 and 1
C. 1 and 0
D. 0 and 0

Question 10 of 25 1.0 Points
The standard deviation of a probability distribution must be:
A. a negative number
B. a number between 0 and 1
C. less than the value of the mean
D. a nonnegative number

Question 11 of 25 1.0 Points
The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:
A. central tendency theorem
B. simple random sample theorem
C. central limit theorem
D. point estimate theorem

Question 12 of 25 1.0 Points
If Z is a standard normal random variable, the area between z = 0.0 and z =1.30 is 0.4032, while the area between z = 0.0 and z = 1.50 is 0.4332. What is the area between z = -1.30 and z = 1.50?
A. 0.0668
B. 0.0968
C. 0.0300
D. 0.8364


Question 13 of 25 1.0 Points
A statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.
77 81 74 77 79 73 80 85 86 73
83 84 81 73 75 91 76 77 95 76
90 85 92 84 81 64 75 90 78 78
82 78 86 86 82 70 76 78 72 93

Compute the standard deviation of these test scores. Place your answer, rounded to 2 decimal places in the blank. For example, 5.34 would be a legitimate entry.

Question 14 of 25 1.0 Points
Find the mean of the following probability distribution?
1 0.20
2 0.10
3 0.35
4 0.05
5 0.30

Place your answer, rounded to two decimal places, in the blank. When entering your answer do not use any labels or symbols other than a decimal point. Simply provide the numerical value. For example, 1.23 would be a legitimate entry.

Question 15 of 25 1.0 Points
In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.

 

Number of Products Purchased
Brands Purchased Fewer Same More Total
Same 10 14 24 48
Changed 262 82 8 352
Total 272 96 32 400

What is the probability that a consumer selected at random purchased fewer products than before? Place your answer, rounded to 4 decimal places, in the blank.

Question 16 of 25 1.0 Points

Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
Number of Vehicles Involved
Did alcohol play a role? 1 2 3
Yes 60 110 30 200
No 40 215 45 300
100 325 75

What proportion of accidents involved alcohol and a single vehicle?
Place your answer, rounded to 2 decimal places, in the blank. For example, 0.23 is a legitimate entry.

Question 17 of 25 1.0 Points

A daily lottery is conducted in which two winning numbers are selected out of 100 numbers. How many different combinations of winning numbers are possible? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.

Question 18 of 25 1.0 Points

The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.

Question 19 of 25 1.0 Points

A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

What is the probability of getting a score between 65 and 89 on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry.

Question 20 of 25 1.0 Points

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend $20 or more at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.

Question 21 of 25 1.0 Points

The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean 6.7 minutes and standard deviation 2.2 minutes. For a door selected at random, what is the probability the assembly line time will be between 5 and 10 minutes? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1776 would be a legitimate answer.

Question 22 of 25 1.0 Points

A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend less than $15 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.

Question 23 of 25 1.0 Points

Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.

What score represents the 60th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.

Question 24 of 25 1.0 Points

Using the standard normal curve, the Z- score representing the 10th percentile is 1.28. True
False

Question 25 of 25 1.0 Points

The left half under the normal curve is slightly smaller than the right half. True
False

Additional Requirements

Level of Detail: Only answer needed

Healthcare Finance

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5.5 You are considering starting a walk-in clinic. Your financial projections for the first year of operations are as follows:

 

Revenues:                                $400,000

Wages & Benefits:                     $220,000

Rent:                                        $5,000

Depreciation:                             $30,000

Utilities:                                     $2,500

Medical Supplies:                      $50,000

Administrative Supplies:             $10,000

 

Assume that all costs are fixed, except supply costs, which are variable. Furthermore, assume that the clinic must pay taxes at a 20 percent rate.

    1. Construct the clinic’s projected P&L statement.

    1. What number of visits is required to break even?

    1. What number of visits is required to provide you with an after-tax profit of $100,000?