1. In general – if price of an item dramatically increases, does demand normally

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1.  In general – if price of an item dramatically increases, does demand normally – A) Increase  B) Decrease  C) Stay the Same

 

2.  In general – if price of an item dramatically decreases, does demand normally – A) Increase  B) Decrease  C) Stay the Same

 

3.  In general – if the supply of an item dramatically increases, does price normally – A) Increase  B) Decrease  C) Stay the Same

4.  In general – if the supply of an item dramatically decreases, does price normally – A) Increase  B) Decrease  C) Stay the Same

 

5.  In general – if the demand of an item dramatically increases, does price normally – A) Increase  B) Decrease  C) Stay the Same

 

6.  In general – if the demand of an item dramatically decreases, does price normally – A) Increase  B) Decrease  C) Stay the Same


7.  In general – if interest rates increase, does the demand for loans by consumers and businesses normally – A) Increase           B) Decrease  C) Stay the Same

8. In general – if interest rates decrease, does the demand for loans by consumers and business normally – A) Increase               B) Decrease  C) Stay the Same

 

A person deposits a certain amount of money in a continuously compounded savings account which

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  1. A person deposits a certain amount of money in a continuously compounded savings account which gives an annual rate of 3.24%. If 15 years later the account shows $4552.24, what was the original amount deposited? Round your answer to the nearest whole dollar.

  2. A person deposits $3550 in a continuously compounded savings account which gives an annual rate of 3.24%. How much money will be in the account in 16 years? Round your answer to the nearest cent.

  3. The population of a species introduced in a new territory is described by the logistic function below. What will the population be in 26 years? Round your answer to the nearest whole number value.

450/1+9e^-0.192t

  1. A sample of 450 grams of radioactive material decays at a continuous rate of 3.2% per year. Find the amount of radioactive material left in the sample after 17 years. Round your answer to the nearest whole gram.

  2. A total of 58 koala bears lived in a preserve in 1999. If their population follows an exponential function with continuous growth of 12.3% per year, estimate the number of koala bears that will be in the preserve in the year 2020. Round your answer to the nearest whole number value.

  3. A piece of ham is removed from a 380 degree Farenheit oven and placed on a cooling rack in the kitchen which is at a constant ambient temperature of 62 degrees Farenheit. Assume that the cooling of the ham follows Newton’s law of cooling, with a characteristic parameter k of 0.114 (per minute). Estimate the ham’s temperature half an hour after it was removed from the oven. Round your answer to one decimal point.

  4. The value of a company’s stock is given by the function below, where “t” is the number of years since the year 2000. Estimate the stock’s value in the year 2009. Round your answer to the nearest whole number value.

V(t)=e^0.582t

  1. A bacteria culture grows at a continuous rate of 2.3% per minute. How many bacteria will there be after 35 minutes, starting with a sample of 2,500,000 bacteria? Round your answer to the nearest whole number value.

 

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1. Which statement is typically NOT true about the alternative hypothesis?

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1.    Which statement is typically NOT true about the alternative hypothesis?

 

a)    It presumes innocence

b)    It is a belief about the population

c)    It is denoted with H sub a.

d)    It focuses on the suspicion of an event.

 

2. Soda Tak claims that Diet Tak has 40mg of sodium per can. You work for a consumer organization that tests such claims. You take a random sample of 60 cans and find that the mean amount of sodium in the sample is 42.4mg. The population standard deviation is 7.2mg. You suspect that there are more than 40mg of sodium per can. Find the z-score.

 

a)    0.2

b)    2.582

c)    2.727

d)    5.143

 

3. Which statemnet below is NOT true about Error Types?

 

a)    A Type I error is when a false null hypothesis is rejected

b)    A Type II error is when a false null hypothesis fails to be rejected

c)    A Type I error is denoted by the Greek letter Alpha

d)    A Type II error is denoted by the Greek letter Beta

 

4. Find the 99% confidence interval for the population mean when the population standard deviation is 4. The sample mean is 6. We assume that the population has a normal distribution Ten items are taken in the sample.

 

a)    3.52 to 8.48

b)    2.74 to 9.26

c)    3.56 to 8.44

d)    4.14 to 7.86

 

5. You test calories for a food item. The brand name has a mean of 158.706 and a sample standard deviation = 25.236, when seventeen are tested. The generic item has a mean of 122.471 and a sample standard deviation = 26.483, when seventeen are tested. Which is a confidence interval of 95%?

 

a)    17.79 to 54.67

b)    18.161 to 54.309

c)    17.01 to 55.46

d)    18.23 to 54.24

 

 

6. There is a new treatment for smokers to stop smoking. In an experiment, 80% of 300 smokers quit after 10 days of the treatment. What is the reasonable age for the success rate p of our new treatment? Which is the 95% confidence interval?

 

a)    0.755 to 0.845

b)    0.8096 to 0.8904

c)    0.8048 to 0.8952

d)    0.749 to 0.851

 

7. Which is the size of the sample needed in order to obtain a margin of error of 3.2% in a 95% Cl for p? That is, we want a proportion plus or minus 3.2%

 

a)    600

b)    702

c)    784

d)    938

 

8.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a)    (1.5179, 999,3)

b)    (0.4882, 999,4)

c)    0.6287, 999,4)

d)    (0.4882, 999,3)

 

 

 

9.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Find the expected frequency for cell ( space) #3 of the contingency table.

 

a)    38.19

b)    42.75

c)    44.77

d)    46.17

A simple linear regression was created to determine GPA based on hours studying per week. You want to know

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1) A simple linear regression was created to determine GPA based on hours studying per week. You want to know if you spend 30 hours per week studying, what range you might expect your GPA to be in. What estimate do you need to calculate to find the range?

Answer 

A. Confidence Interval Estimate

B. Point Estimate

C. Residual Interval Estimate

D. Prediction Interval Estimate

 

2)The Coefficient of Determination for a simple linear regression is 0.87 and the b1 came out to be -1.58. What is the Sample Correlation Coefficient and what does it mean?

Answer 

A. -0.93 and it means there is a negative linear correlation between x and y.

B. 1.26 and it means there is a positive linear correlation between x and y.

C. -0.93 and it means there is no linear correlation between x and y.

D. 1.26 and it means there is no linear correlation between x and y.

3)The degrees of freedom used to calculate the p-value of the goodness of fit of a multinomial distribution is …

Answer 

A. k-3

B. n-3

C. n-1

D. k-1 

4)X-ray Express wants to simulate the arrival of requests. They think the arrivals per day follow a Poisson distribution and they have collected a sample of arrivals per day for 100 days to confirm. The information is provided in Figure 2 and the average number of arrivals is 1.2 for the 100 samples. 

What is the chi squared statistic for the given information? 

Answer 

A. 4.29

B. 2.38

C. 25

D. 2.84

5)X-ray Express wants to simulate the arrival of requests. They think the arrivals per day follow a Poisson distribution and they have collected a sample of arrivals per day for 100 days to confirm. The information is provided in Figure 2 and the average number of arrivals is 1.2 for the 100 samples. 

 

The p-value of the chi squared statistic is 0.304 and the desired alpha level is 0.05. Should X-Ray Express use a Poisson distribution in their simulation? (Does the data fit a Poisson distribution?) 

Answer 

A. No they cannot use a Poisson distribution because the null hypothesis is not rejected

B. Yes they can use a Poisson distribution because the null hypothesis is not rejected.

C. No they cannot use a Poisson distribution because the null hypothesis is rejected

D. Yes they can use a Poisson distribution because the null hypothesis is rejected

 

x= 16,29,29,48,56

y=11,13,14,17,20

 

that’s figure 1

6)Figure 1 contains information on annual income and years of education. The independent variable is years of education and the dependent variable is income.

 

Develop the least squares equation regression equation.

Answer 

A. y(hat) = 4.5-31.9x

B. y(hat) = 35.6-15x

C. E(y) = 4.5x-31.9

D. y(hat) = -31.9+4.5x

 

7)Figure 1 contains information on annual income and years of education. The independent variable is years of education and the dependent variable is income.

 

Estimate the yearly income for an individual with 19 years of education.

Answer 

A. $53,600

B. $249,400

C. -$601,600

D. $56,000

 

 

8)Figure 1 contains information on annual income and years of education. The independent variable is years of education and the dependent variable is income.

 

With an alpha of 0.05 what is the test statistic to determine if the slope (beta 1) is significant? Sb1=0.4374 If the p-value for the test statistic works out to be 0.00196 is the slope (beta 1) significant?

Answer 

A. t-stat = 73.0 and it is significant.

B. t-stat = 10.3 and it is significant.

C. t-stat = 73.0 and it is not significant.

D. t-stat = 10.3 and it is not significant. 

 

 

9)X-ray Express wants to simulate the arrival of requests. They think the arrivals per day follow a Poisson distribution and they have collected a sample of arrivals per day for 100 days to confirm. The information is provided in Figure 2 and the average number of arrivals is 1.2 for the 100 samples. 

 

X-Ray Express wants to know during the 250 working days per year how many of those days they should expect to see 1 request arrive. (e^(-1.2)=0.3012) How many days per year should they expect to see 1 request arrive?

Answer 

A. 36

B. 0.361

C. 90

D. 30

 

study the following table of joint probabilities was produced

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The issue of health-care coverage in the United States is becoming a critical issue in American politics. A large-scale study was undertaken to determine who is and is not covered. From this study the following table of joint probabilities was produced.

Age Category

Has Health Insurance

Does Not Have Health Insurance

25-34

0.167

0.085

35-44

0.209

0.061

45-54

0.225

0.049

55-64

0.177

0.026

 

If one person is selected at random, find the following probabilities.

a. P (Person has health insurance) = b. P (Person 55-64 has no health insurance) =
c. P (person without health insurance is between 25 and 34 years old)

1.Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George

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1.Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?

Hypothesis Test: Independent Groups (t-test, pooled variance)

Larry

George

 

4.77

5.02

mean

1.05

1.23

std. dev.

40

50

n

88

df

 

-0.25

difference (Larry – George)

 

1.33102

pooled variance

 

1.1537

pooled std. dev.

 

0.24474

standard error of difference

 

0

hypothesized difference

 

-1.02

t

 

0.3098

p-value (two-tailed)

 

-0.73636

confidence interval 95.% lower

 

0.23636

confidence interval 95.% upper

 

0.48636

margin of error

 

 

In order to estimate the difference between the yearly incomes of marketing managers in the east and the west

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In order to estimate the difference between the yearly incomes of marketing managers in the east and the west, the following information was gathered:

East                                                                            West

n1= 40                                                               n2= 45

x1= 72 (in $1000)                                             x2= 78 (in $1000)

s1= 6 (in $1,000)                                               s2= 8 (in $1000)

DF= 80

1. What is the point estimate between the two population means?

2. At 90% confidence, what is the margin of error?

3. What is the 90% confidence interval for the difference between the two population means?

4. Use P-value approaches to test to determine if the yearly average income of marketing managers in the East is significantly different from the west. a= 0.10

a) State the Null and Alternative Hypotheses

b) what is the value of the test statistic?

c) What is the critical value?

d) what is the p-value?

e) what is your conclusion regarding the null hypothesis?

 

Create the ANOVA table using Excel or Minitab.

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Consider the following data. X = Weekly Advertising expenditures and Y = Weekly Sales.

(worth 24 points total)

Y

X

1260

42

1390

55

1435

63

1435

55

1460

49

1310

47

1410

63

1520

62

1585

65

1660

72

 

a)         Create the ANOVA table using Excel or Minitab.                

b)         What is the prediction equation?                    ?         

c)         What is your prediction of sales if you spend $50 on advertising?                ?         

d)         Does the amount of advertising expenditures have any relationship to sales?                                              

First, you discuss Location – but the table and commentary do not match. In the table

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First, you discuss Location – but the table and commentary do not match.  In the table
you make it sound like there are 100 in the sample, when in reality there are only 50. 
The bar graph is correct.   (Same exact comments apply to the variable SIZE) 

For the variable INCOME, you list a  lot of descriptive statistics, and they are all correct. 
But some are not explained – e.g. your statement
“kurtosis coefficient is negative implies that the height of the distribution is less than normal.”
is really unclear.   If you do not understand kurtosis, it is better not to mention it (it will be hard 
to explain to the client in any case).    The SD and range are not measures of central tendency, 
they are measures of variation – and the coefficient of determination is a good one to mention, 
but it is NOT 30.17,  it is 30.17%.  And again you should not mention it at all if it is not explained. 
(It is the ratio of the SD to the mean;  so the SD is only about 3/10 the size of the mean).

 

For the first pairing, the graph used is not appropriate;  a scatterplot should NOT be used when 
one of the variables is categorical.   And the concept of a “positive relationship” would not make 
any sense in this context.   Moreover, the statement
“I can conclude all locations are approximately expected to have almost same income level”
cannot be supported by your graph.   What would have worked here would have been a simple bar 
graph with a bar for each location and the height being either the median income or mean income. 
Had you done this, you would see that there is indeed a significant difference in the average incomes. 

For the other two pairings, the scatterplots are okay. 
And again you should not be quoting statistics like “rho” if you do not know what they mean!  
The Pearson product moment coefficient would probably be easy to explain to the clients;  but
either you should actually explain it or leave it out. 

Given the following data for a community health center, calculate the average and marginal

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  1. Given the following data for a community health center, calculate the average and marginal cost for each output level and (in case of marginal cost) between successive output levels.

Number of visits                                 Total cost

1                                                                                                                    $100

2                                                                                                                    160

3                                                                                                                    200

4                                                                                                                    260

5                                                                                                                    360