(d). Describe the sampling distribution of the sample mean, specifically, the mean and standard deviation
(Hint: = 7.75).

(b). Find the probability of a false positive, that the test is positive, given that the person is disease-free.

(a). Please define the population of interest in this question.

(b). Explain what is a sampling distribution of a mean?

(c). Explain what is Central Limit Theorem?

(e). Within what limits would you expect the sample average to lie, with probability .95?

(f). Calculate the probability that the sample mean is greater than $73,000?

(g). If your random sample actually produced a sample mean of $73,000, would you consider this unusual? What conclusion might you draw?

4. (10 points in total) Suppose that the word-association experiment is conducted using eight people as blocks and making a comparison of reaction times within each person； that is, each person is subjected to both stimuli in a random order. The reaction times (in seconds) for the experiment are as follows: Comment on the use of paired observations to estimate the difference between two population means  rather than estimation based on independent random samples selected from the two populations (unpaired design). Why is a paired experiment often preferable? Explain.

(a) First indicate the null and alternative hypotheses for this research question.

(b) Construct a 95% confidence interval for the slope. Discuss how the critical value of the confidence interval are determined.