107年 - 107 陽明交通大學管碩士班考試入學試題：統計學#123984

(a). The sample space S (call these four tablets as C₁, C₂, A₁ and A₂).

(b). Find the probability that an event A that neither patient obtained a cold tablet.

(a). Use the definition of conditional probability to find P(D|N).

(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?

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

(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.

(c) Interpret the meaning of the slope estimated, and test the hypothesis that β = 0 at the 5% level of significance.

(d) Ideally, how the plot of residuals should look like? Explain.

6. (15 points in total) A survey was conducted to determine student, faculty, and administration attitudes about a new university parking policy. The distribution of those favoring or opposing the policy is shown in the table. Do the data provide sufficient evidence to indicate that attitudes about the parking policy are independent of student, faculty, or administration status?