Suppose we are comparing two populations to see if they have the same mean. A sample from each population is taken and the difference in means was 12. Suppose a test of the hypothesis that the difference is zero has a p-value of 0.0156. Which of the following are true statements (list all that are true): a. The two-sided 99% confidence interval includes zero. b. The one-sided 99% confidence interval includes zero. c. The hypothesis that they are equal would be rejected at a 95% confidence level against the alternative that they are not. d. The hypothesis that they are equal would be rejected at a 99% confidence level against the alternative that they are not.
a. The two-sided 99% confidence interval includes zero.
Answer: True
It is true because p-value = 0.0156 is greater than corresponding alpha value 0.01.
b. The one-sided 99% confidence interval includes zero.
Answer: False
It is false because corresponding p-value would be half of 0.0156 which will be less than alpha value 0.01.
c. The hypothesis that they are equal would be rejected at a 95% confidence level against the alternative that they are not.
Answer: True
It is true because p-value = 0.0156 will be less than corresponding alpha value 0.05.
d. The hypothesis that they are equal would be rejected at a 99% confidence level against the alternative that they are not.
Answer: False
...because p-value will be less than 0.01.
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