1. What is the parameter of interest to compare the proportions from two populations?

p1+ p2

p1- p2

p1+ p2

p1- p2

1+ 2

1 -2

^{The following scenario applies to questions 2-7:}

^{In the 1980's, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of 22,071 medical doctors participating in the study, 11,037 were randomly assigned to take aspirin and 11,034 were randomly assigned to the placebo group. Doctors in this group were given a sugar pill disguised to look like aspirin. After six months, the proportion of heart attacks in the two groups was compared. Only 104 doctors who took aspirin had a heart attack, whereas 189 who received the placebo had a heart attack. Can we conclude from this study that taking aspirin reduced the chance of having a heart attack? The purpose of this study was to determine whether taking an aspirin daily reduces the proportion of heart attacks.}

2. What proportion of those who received the placebo had a heart attack?

0.005

0.009

0.017

0.55

3. Were the data appropriately collected for performing a two-sample z test on proportions?

Yes, because the 22,071 subjects were randomly selected from all medical doctors.

Yes, because the 22,071 subjects in the study were randomly allocated to either the aspirin group or the placebo group.

No, because there is no random sampling.

No, because the 22,071 subjects in the study were not randomly allocated to either the aspirin group or the placebo group.

4. Is the normality of the sampling distribution condition for performing a two-sample z test on proportions met?

No, because one or both of the population distributions were not stated to have a known normal distribution

No, because at least one of the np checks is less than 5

Yes, because 22,071 is greater than 30

Yes, because all of the np checks are greater than 5

5. Suppose the test statistic was -3.17. What is the associated p-value?

0.0008

0.0010

0.0020

0.9992

6. Suppose the p-value was 0.034. What conclusion should we make at=0.05?

Fail to reject the null hypothesis and say that we have insufficient evidence to conclude that the true proportion of heart attacks for those who take aspirin is less than those who take a placebo

Fail to reject the null hypothesis and say that we have sufficient evidence to conclude that the true proportion of heart attacks for those who take aspirin is less than those who take a placebo

Reject the null hypothesis and say that we have insufficient evidence to conclude that the true proportion of heart attacks for those who take aspirin is less than those who take a placebo.

Reject the null hypothesis and say that we have sufficient evidence to conclude that the true proportion of heart attacks for those who take aspirin is less than those who take a placebo.

7. A 90% confidence interval was found to be (-0.45, -0.13). Suppose that we were instead testing a two-sided hypothesis. Does this confidence interval allow us to say that the two proportions differ significantly at= 0.10?

Yes, because the confidence interval includes 0.

Yes, because the confidence interval does not include 0.

No, because the confidence interval includes 0.

No, because the confidence interval does not include 0.