1. You choose an alpha level of .01 and then analyze your data.
a. What is the probability that you will make a Type I error given that the null hypothesis is true?
b. What is the probability that you will make a Type I error given that the null hypothesis is false?
2. True/false: It is easier to reject the null hypothesis if the researcher uses a smaller alpha (α) level.
3. Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data.
a b c
4 6 7
3 7 8
2 8 5
1 4 7
4 6 9
2 4 2
a. Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.
b. Compute a one-sample t-test on this column (with the L values for each subject) you created.
4. You are conducting a study to see if students do better when they study all at once or in intervals. One group of 12 participants took a test after studying for one hour continuously. The other group of 12 participants took a test after studying for three twenty minute sessions. The first group had a mean score of 75 and a variance of 120. The second group had a mean score of
86 and a variance of 100.
a. What is the calculated t value? Are the mean test scores of these two groups significantly different at the .05 level?
b. What would the t value be if there were only 6 participants in each group?
Would the scores be significant at the .05 level?
5. 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
CHAPTER 10 | HYPOTHESIS TESTING WITH TWO SAMPLES 557
Relaxed time (seconds) Jumping time (seconds)
23 25
45 43
37 35
29 32
6. A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.
