A doctor claims that the mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night. To investigate, he selects a random sample of 50 high school seniors from all high schools in his county. He also selects a random sample of 50 seniors from the colleges in his county. He constructs a 95% confidence interval for the true mean difference in the number of hours of sleep for seniors in high school and seniors in college. The resulting interval is (0.57, 1.25). Based upon the interval, can the doctor conclude that mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night?
Answer
A
yes because 1 is in the confidence interval
B
yes because 0 is not in the confidence interval
C
no because 1 is in the confidence interval
D
no because 0 is not in the confidence interval
Explanation
The confidence interval for the mean difference is (0.57, 1.25), which does not include 0. A difference of 0 would mean the two groups have equal mean sleep hours, so the interval supports concluding that their means differ. The correct choice is yes because 0 is not in the confidence interval.
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