1. Elaborate on what is meant by *degrees of freedom*. Use an example.

2. A sample set of 29 scores has a mean of 76 and a standard deviation of 7. Can we accept the hypothesis that the sample is a random sample from a population with a mean greater than 72? Use

*α=*0.011 tail in making your decision.

3. Using each of the following random samples, determine

the 95% and 99% confidence intervals for the

population mean:

a. *X*obt =25, *s *=6, *N *=15

b. *X*obt =120, *s *= 8, *N *=30

c. *X*obt =30.6, *s * =5.5, *N *=24

d. Redo part **a **with *N *=30. What happens to the confidence interval as *N *increases?

4. A physician employed by a large corporation believes that due to an increase in sedentary life in the past decade, middle-age men have become fatter. In 1995, the corporation measured the percentage of fat in their employees. For the middle-age men, the scores were normally distributed, with a mean of 22%. To test her hypothesis, the physician measures the fat percentage in a random sample of 12 middle-age men currently employed by the corporation. The fat percentages found were as follows: 24, 40, 29, 32, 33, 25, 15, 22, 18, 25, 16, 27. On the basis of these data, can we conclude that middle-age men employed by the corporation have become fatter? Assume a directional

*H*1 is legitimate and use *α = *0.051 tail in making your decision.

5. You are interested in determining whether an experimental birth control pill has the side effect of changing blood pressure. You randomly sample ten women from the city in which you live. You give five of them a placebo for a month and then measure their diastolic blood pressure. Then you switch them to the birth control pill for a month and again measure their blood pressure. The other five women receive the same treatment except they are given the birth control pill first for a month, followed by the placebo for a month. The blood pressure readings are shown here. Note that to safeguard the women from unwanted pregnancy, another means of birth control that does not interact with the pill was used for the duration of the experiment.

experiment.

** Diastolic Blood Pressure**

**Subject No. ***Birth controlpill Placebo*

1 108 102

2 76 68

3 69 66

4 78 71

5 74 76

6 85 80

7 79 82

8 78 79

9 80 78

10 81 85

6. The manager of the cosmetics section of a large department store wants to determine whether newspaper advertising really does affect sales. For her experiment, she randomly selects 15 items currently in stock and proceeds to establish a baseline. The 15 items are priced at their usual competitive values, and the quantity of each item sold for a 1-week period is recorded. Then, without changing their price, she places a large ad in the newspaper, advertising the 15 items. Again, she records the quantity sold for a 1-week period. The results follow.

**Item No. Sold** **No. Sold**

** Before Ad After Ad**

** **

1 25 32

2 18 24

3 3 7

4 42 40

5 16 19

6 20 25

7 23 23

8 32 35

9 60 65

10 40 43

11 27 28

12 7 11

13 13 12

14 23 32

15 16 28

7. An educator wants to determine whether early exposure to school will affect IQ. He enlists the aid of the parents of 12 pairs of preschool-age identical twins who agree to let their twins participate in this experiment. One member of each twin pair is enrolled in preschool for 2 years while the other member of each pair remains at home. At the end of the 2 years, the IQs of all the children are measured. The results follow.

** Pair**

** Twin at Preschool Twin at home**

1 110 114

2 121 118

3 107 103

4 117 112

5 115 117

6 112 106

7 130 125

8 116 113

9 111 109

10 120 122

11 117 116

12 106 104

8. Discuss how the t-test for correlated groups and the t-test for single samples are alike and different.

9. Explain why using the t statistic may be an appropriate alternative to using a z-score (use the concept of estimated standard error to justify your answer).

Subject | Mathematics |

Due By (Pacific Time) | 11/22/2014 01:00 pm |

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