## 5. 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 & gt; 500 at level 0.05.

5. 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 & gt; 500

at level 0.05. To do so, he computes that 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.