Questions 25 through 29 are based on the following scenario.
In an attempt to compare cell damage resulting from exposure to the sun, 9 subjects had one arm exposed to solar radiation and the other arm covered. Skin cells from both arms were studied and the level of some chemical, related to skin damage, was recorded. Summary data revealed the following:
Sample Mean
Sample Standard Deviation
Exposed Arm
15.2
16
Unexposed Arm
14.0
14
The differences (exposed – unexposed) can be assumed to be normally distributed, and the sample standard deviation of the 9 differences is .
25.Is this a paired design or a two independent samples design?
26.Calculate a 95% confidence interval for the mean difference (exposed – unexposed).
27.Is it correct to say that 95% of the time the population mean difference will lie in the confidence interval you found in question 22? Explain.
28.All nine subjects had their right arm exposed and their left arm covered. The design of this study could be improved. What would you randomize in the study?
29.The p-value for testing if the solar exposure increases cell damage is found to be 0.003. Is it correct to say that the probability that the null hypothesis is true is 0.003?
Questions 30 and 31 are based on the following scenario.
A therapist believes that the number of negative self-references made by depressed clients will decrease after therapy. To test this hypothesis, the therapist records the number of negative self-references before and after a three-month therapy program. A paired T-test was conducted to test the hypothesis . The observed test statistic value was 2.5.
30.The value of the observed test statistic says something about the location of the sample mean difference. Explain what the value means.
31.The standard error of was 1.2. Explain what the standard error measures.
Questions 32 through 35 are based on the following scenario.
A quality control engineer wanted to compare two different production lines with respect to the proportion of defective items produced. The two production lines, Line 1 and Line 2, produce the same part. A random sample of 200 parts produced by Line 1 was obtained and there were 14 defective items found. There were 10 defectives in an independent random sample of 200 parts produced by Line 2.
32.Calculate a 95% confidence interval for the difference between the proportions of defectives (Line 1 – Line 2).
33.Interpret the confidence interval given in question 28.
34.Interpret the 95% level of confidence used in question 28.
35.If the engineer had sampled 10 parts from each production line, would the corresponding confidence interval (computed in the same way as in question 28) have been valid? Explain your answer.