1. A recent study investigated the extent to which hypertension is affected by alcohol consumption. Among other things, the study compared the rate of hypertension in nondrinkers to the rate in people that are moderate beer drinkers (average between 0.5 and 1 glass of beer per day). They found that a 95% confidence interval for the relative risk of hypertension in moderate beer drinkers as compared to nondrinkers was 0.47 to 0.90. A relative risk of 1 means that the two groups have the same risk of hypertension, while a relative risk of less than 1 means that moderate beer drinkers have less risk of hypertension than nondrinkers. If the researchers who ran the study had tested the hypotheses
H0: the relative risk for moderate beer drinkers as compared to nondrinkers = 1
Ha: the relative risk for moderate beer drinkers as compared to nondrinkers ≠ 1
they would have concluded which of the following?
A. reject H0 at level 0.10
B. fail to reject H0 at level 0.10
C. Neither choice is correct. We cannot determine what we would do at level α = 0.10 because the interval given is a 95% confidence interval, not a 90% confidence interval.
2. The teacher of a class of 40 high school seniors is curious whether the mean Math SAT score μ for the population of all 40 students in his class is greater than 500 or not. To investigate this, he decides to test the hypotheses
H0: μ = 500 Ha: μ > 500
at level α = 0.05. To do so, he computes the average Math SAT score of all the students in his class and constructs a 95% confidence interval for the population mean. The mean Math SAT score of all the students was 502 and, assuming the standard deviation of the scores is α = 100, he finds the 95% confidence interval is 502 ± 31. He may conclude
A. H0 cannot be rejected at level α = 0.05 because 500 is within confidence interval.
B. H0 cannot be rejected at level α = 0.05, but this must be determined by carrying out the hypothesis test rather than using the confidence interval.
C. We can be certain that H0 is not true.