A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test whether this claim is true, you randomly sample 100 doctors and ask their preference. Of these 100 doctors, 80 indicate that they recommend aspirin.

(a) [1 pt] Which of the following is the appropriate test to use in this situation?

A. Two-sample, one-sided Z-test of proportions

B. One-sample, one-sided Z-test of a proportion

C. Two-sample, two-sided Z-test of proportions

D. One-sample, two-sided Z-test of a proportion

Answer:

(b) [1 pt] State the null and alternative hypotheses of the test.

(c) [1 pt] Which of the options below is the correct decision rule for the test?

1. Reject H₀ if the test statistic is smaller than the critical value.
2. Reject H₀ if the test statistic is larger than the critical value.
3. Reject H₀ if the test statistic is either larger than the upper critical value or smaller than the lower critical value.
4. None of the above.

Answer:

(d) [2 pts] Calculate the test statistic and make a decision for whether you reject H₀ or fail to reject H₀ at the ? = 0.05 significance level.

(e) [2 pts] Calculate a 95% confidence interval around the point estimate. Can this confidence interval be used to test the claim that 9 out of 10 doctors recommend aspirin for patients with headaches?In a sentence or two, explain why or why not.

Problem #2

Problem #2 Karl Pearson, who developed many important concepts in statistics, collected crime data in 1909. Of those convicted of arson, 50 were drinkers and 43 abstained. Of those convicted of fraud, 63 were drinkers and 144 abstained. (a) [3 pts] Arrange the data into a 2 x 2 table given below, and compute the estimated proportions p, = proportion of drinkers amongst convicted arsonists and p, = the proportion of drinkers among those convicted of fraud, as well as p = the overall proportion of drinkers amongst both types of criminals. Drinkers Abstainers Total Convicted of Arson Convicted of Fraud Total (b) [1 pt] Suppose one wanted to test whether there was a difference between p, and p2, the (unknown) population proportions of drinkers amongst those convicted of arson and those convicted of fraud, respectively. Which of the following tests below would be appropriate? (More than one answer may be correct.) A. One-sample, one-sided Z-test of a proportion B. Two-sample, two-sided Z-test of proportions C. Pearson chi-square test D. One-sample, two-sided Z-test of a proportion Answer: (c) [1 pt] State the null and alternative hypotheses of the test