# Introduction to Statistics

CHAPTER 9

74. A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, is the data highly inconsistent with the claim?

Chapter 10

80. At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.

Relaxed time (seconds) Jumping time (seconds)

26                                              21

47                                              40

30                                                28

22                                                 21

82.  Marketing companies have collected data implying that teenage girls use more ring tones on their cellular phones than teenage boys do. In one particular study of 40 randomly chosen teenage girls and boys (20 of each) with cellular phones, the mean number of ring tones for the girls was 3.2 with a standard deviation of 1.5. The mean for the boys was 1.7 with a standard deviation of 0.8. Conduct a hypothesis test to determine if the means are approximately the same or if the girls’ mean is higher than the boys’ mean.

90. Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of six. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of eight. Is the mean age of entering prostitution in Canada lower than the mean age in the United States? Test at a 1% significance level.

120.  A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four new students. She records their 18-hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as follows.

Player 1 Player 2 Player 3 Player 4

Mean score before class 83            78             93              87

Mean score after class    80            80             86             86

The correct decision is:

a. Reject H0.

b. Do not reject the H0

CAHPTER 12:

8. Participants threw darts at a target. In one condition, they used their preferred hand; in the other condition, they used their other hand. All subjects performed in both conditions (the order of conditions was counterbalanced). Their scores are shown below.

Preferred Non-preferred

12                     7

7                          9

11                       8

13                     10

10                        9

a. Which kind of t-test should be used?

b. Calculate the two-tailed t and p values using this t test.

c. Calculate the one-tailed t and p values using this t test.

12. If you have 5 groups in your study, why shouldn’t you just compute a t test of each group mean with each other group mean?

CHAPTER 13:

4. What does the standard error of the estimate measure? What is the formula for the standard error of the estimate?

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