A study was conducted to determine the true mean number of hours of television watched on school nights by teenagers. A 99 percent confidence interval for the true mean is 0 point 8 hours to 2 point 1 hours. Based upon this interval, what conclusion should be made about the hypotheses: ratio of cap h sub 0 to mu is equal to 2 point 5 versus ratio of cap h sub A to mu is not equal to 2 point 5 where μ= the true mean number of hours of television watched on school nights by teenagers at α=0.01 ?
Answer
A
Fail to reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
B
Reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is not convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
C
Reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
D
Fail to reject cap h sub 0 . Since 2 point 5 falls outside the 99 percent confidence interval, there is not convincing evidence that the true mean number of hours of television watched on school nights by teenagers differs from 2 point 5 hours.
Explanation
The 99% confidence interval is 0.8 to 2.1 hours, and the hypothesized mean of 2.5 hours is outside that interval. For a two-sided test at α = 0.01, a hypothesized value outside the matching 99% confidence interval leads us to reject the null hypothesis. Thus, there is convincing evidence that the true mean number of hours differs from 2.5 hours; this is choice C.
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