Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. = 0.05 for a two-tailed test.
±2.575
1.764
±1.96
±1.645
Question 2
Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. = 0.09 for a right-tailed test.
±1.96
1.34
±1.96
1.34
±1.34
1.96
Question 3
Find the value of the test statistic z using z = The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 681 drowning deaths of children with 30% of them attributable to beaches.
3.01
3.01
2.85
-2.85
-3.01
Question 4
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a left-tailed test is z = -1.83.
0.0672; reject the null hypothesis
0.0336; reject the null hypothesis
0.9664; fail to reject the null hypothesis
0.0672; fail to reject the null hypothesis
Question 5
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a two-tailed test is z = -1.63.
0.1032; fail to reject the null hypothesis
0.0516; reject the null hypothesis
0.0516; fail to reject the null hypothesis
0.9484; fail to reject the null hypothesis
Question 6
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
There is not sufficient evidence to support the claim that the mean attendance is less than 694.
There is sufficient evidence to support the claim that the mean attendance is greater than 694.
There is sufficient evidence to support the claim that the mean attendance is less than 694.
There is not sufficient evidence to support the claim that the mean attendance is greater than 694.
Question 7
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A medical researcher claims that 6% of children suffer from a certain disorder. Identify the type I error for the test.
Reject the claim that the percentage of children who suffer from the disorder is different from 6% when that percentage really is different from 6%.
Reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.
Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.
Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually different from 6%.
Question 8
Find the P-value for the indicated hypothesis test. In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.
0.2843
-0.2843
0.2157
0.5686
Question 9
Find the critical value or values of based on the given information. H0: = 8.0 n = 10 = 0.01
2.088, 21.666
1.735, 23.589
23.209
21.666
Question 10
Find the critical value or values of based on the given information. H1: > 3.5 n = 14 = 0.05
22.362
22.362
5.892
24.736
23.685
5.892

MAT540

Week 10 Homework

Chapter 6

4. Consider the following transportation problem:

From To (cost) Supply

1 2 3 

A $ 6 $ 9 $100 130

B 12 3 5 70

C 4 8 11 100

Demand 80 110 60 

Formulate this problem as a linear programming model and solve it by using the computer.

6. Consider the following transportation problem:

From To (cost) Supply

1 2 3 

A $ 6 $ 9 $ 7 130

B 12 3 5 70

C 4 8 11 100

Demand 80 110 60 

Solve it by using the computer.

36. World Foods, Inc., imports food products such as meats, cheeses, and pastries to the United States from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports deliver the products to Norfolk, New York and Savannah, where they are stored in company warehouses before being shipped to distribution centers in Dallas, St. Louis and Chicago. The products are then distributed to specialty foods stores and sold through catalogs. The shipping costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.) at the European ports are provided in the following table:

From To (cost) Supply

4. Norfolk 5. New York 6. Savannah 

1. Hamburg $420 $390 $610 55
2. Marseilles 510 590 470 78
3. Liverpool 450 360 480 37

The transportation costs ($/1,000 lb.) from each U.S. city of the three distribution centers and the demands (1,000 lb.) at the distribution centers are as follows:

Warehouse Distribution Center

7. Dallas 8. St. Louis 9. Chicago
4. Norfolk $ 75 $ 63 $ 81
5. New York 125 110 95
6. Savannah 68 82 95

Demand 60 45 50

Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs.

48. The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) required by each salesperson to cover each city is shown in the following table:

Region (days)

Sales-person A B C D E

1 17 10 15 16 20

2 12 9 16 9 14

3 11 16 14 15 12

4 14 10 10 18 17

5 13 12 9 15 11

Which salesperson should be assigned to each region to minimize total time? Identify the optimal assignments and compute total minimum time.

Question 1

 

A ‘rare’ outcome, due to an extreme value found for the sample mean relative to the population mean, signifies that the null hypothesis should be:

 

a.         retained

b.         rejected

c.         accepted

d.         none of the above

 

 

Question 2

 

To express a sample mean as a Z value:

 

a.         subtract the hypothesized population mean.

b.         subtract the hypothesized population mean and divide by the standard deviation.

c.         subtract the hypothesized population mean and divide by the standard error of the mean.

d.         subtract the hypothesized population mean and divide by the variance.

 

 

Question 3

 

Given critical z values of ±1.96 and an observed z value of -2.40, the appropriate decision is to:

 

a.         neither retain nor reject, but conduct another investigation

b.         neither retain nor reject, but increase the size of the sample

c.         reject the null hypothesis

d.         retain the null hypothesis

 

 

Question 4

Given an observed difference between a sample mean of 42 and a hypothesized population mean of 50, you:

 

a.         must determine whether this observed difference can reasonably be attributed to chance

b.         can retain, but not accept, the null hypothesis

c.         can conclude that the alternative hypothesis is true

d.         can conclude that the null hypothesis is true

 

 

Question 5

A decision to reject the null hypothesis implies that:

 

a.         there is a lack of support for the alternative hypothesis

b.         there is support for the alternative hypothesis

c.         the sample is probably not representative

d.         the sample size is probably too small

e.         none of the above

 

 

Question 6

Compared to a two-tailed hypothesis test, a one-tailed test is more likely to detect a:

 

a.         true null hypothesis in the direction of concern

b.         false null hypothesis

c.         false null hypothesis in the direction of concern

d.         true null hypothesis

 

 

Question 7

When the rejection of a true null hypothesis would have unusually disastrous consequences, it is best to set your level of significance equal to:

 

a.         .10

b.         .05

c.         .01

d.         .001

 

Question 8

If your observed sample mean were exactly equal to your population mean (assuming some moderate variation in both the sample and the population), then your z value would be:

 

1.         1.96

2.         1.65

3.         2.58

4.         0

5.         not enough information to determine

 

 

 

 

Question 9

 

In an experiment to determine whether TV cartoons produce more aggressive behavior in grade school children, the null hypothesis would state that TV cartoons have:

 

a.         a statistically significant effect on aggressive behavior

b.         only a slight effect on aggressive behavior

c.         an effect on aggressive behavior

d.         no effect on aggressive behavior

 

 

Question 10

 

If the null hypothesis is in reality false, and the z value of the randomly selected sample doesn’t deviate beyond the critical z value, the null hypothesis will be:

 

1.         correctly retained

2.         correctly rejected

3.         incorrectly retained

4.         incorrectly rejected

 

Question 11

Two ways to increase the likelihood of detecting a real effect are to _______ sample size and to _______ alpha.

 

a.         decrease; decrease

b.         decrease; increase

c.         increase; decrease

d.         increase; increase

 

Question 12

 

You’re testing a new vitamin pill that could save many lives if it works even a little bit, and would do no harm even if it did not have any real effect. Given that there is often a trade off between risking Type I and Type II error, which type should you concentrate on minimizing in this situation?

 

a.         Type I error

b.         Type II error

c.         both Type I and Type II error are equally bad

d.         Type III error; I don’t know what it is, but I don’t like it

 

 

Question 1. 1. According to the following graphic, X and Y have _________.
(Points : 3)
strong negative correlation
virtually no correlation
strong positive correlation
moderate negative correlation
weak negative correlation

Question 2. 2. A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a function of batch size (the number of boards produced in one lot or batch). The independent variable is ______. (Points : 3)
batch size
unit variable cost
fixed cost
total cost
total variable cost

Question 3. 3. A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch). The intercept of this model is the ______. (Points : 3)
batch size
unit variable cost
fixed cost
total cost
total variable cost

Question 4. 4. If x and y in a regression model are totally unrelated, _______. (Points : 3)
the correlation coefficient would be -1
the coefficient of determination would be 0
the coefficient of determination would be 1
the SSE would be 0
the MSE would be 0sQuestion 5. 5. A manager wishes to predict the annual cost (y) of an automobile based on the number of miles (x) driven. The following model was developed: y = 1,550 + 0.36x.
If a car is driven 10,000 miles, the predicted cost is ____________. (Points : 3)
2090
3850
7400
6950
5150Question 6. 6. A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch), production plant (Kingsland, and Yorktown), and production shift (day and evening). In this model, “shift” is ______. (Points : 3)
a response variable
an independent variable
a quantitative variable
a dependent variable
a constant

Question 7. 7. A multiple regression analysis produced the following tables: Predictor
Coefficients
Standard Error
t Statistic
p-valueIntercept
The regression equation for this analysis is ____________. (Points : 3)

 

 

7. A multiple regression analysis produced the following tables:
 

Predictor	Coefficients	Standard Error	t Statistic	p-value
Intercept	616.6849	154.5534	3.990108	0.000947
x1	-3.33833	2.333548	-1.43058	0.170675
x2	1.780075	0.335605	5.30407	5.83E-05

 

Source	df	SS	MS	F	p-value
Regression	2	121783	60891.48	14.76117	0.000286
Residual	15	61876.68	4125.112
Total	17	183659.6

 

 

 

 

 

These results indicate that ____________. (Points : 3)
none of the predictor variables are significant at the 5% level
each predictor variable is significant at the 5% level
x1 is the only predictor variable significant at the 5% level
x2 is the only predictor variable significant at the 5% level
the intercept is not significant at the 5% level

Question 9. 9. A real estate appraiser is developing a regression model to predict the market value of single family residential houses as a function of heated area, number of bedrooms, number of bathrooms, age of the house, and central heating (yes, no). The response variable in this model is _______. (Points : 3)
heated area
number of bedrooms
market value
central heating
residential houses

 

Question 10. 10. In regression analysis, outliers may be identified by examining the ________. (Points : 3)
coefficient of determination
coefficient of correlation
p-values for the partial coefficients
residuals
R-squared value

From the time of early studies by Sir Francis Galton in the late nineteenth century linking it with mental ability, the cranial capacity of the human skull has played an important role in arguments about IQ, racial differences, and evolution, sometimes with serious consequences.  (See, for example, S.J. Gould, “The Mismeasure of Man,” 1996.)    

  Suppose that the mean cranial     capacity measurement for modern, adult males is  

1041 cc (cubic centimeters).    

  Complete    the following statements about the distribution of cranial capacity measurements for modern, adult males. 

          (a) According to Chebyshev’s theorem, at least ?56%75%84%89% of the measurements lie within 2 standard deviations of the mean, 1041cc.

(b) Suppose that the distribution is bell-shaped.  If approximately 99.7% of the measurements lie between 309 cc and 1773 cc, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is .