Statistics Question?

The following five questions (i.e., questions 2-6) refer to the following information:





A study was conducted in order to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours.


A similar study conducted a year earlier estimated that μ, the mean number of weekly hours that U.S. adults use computers at home to be 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since last year.





Using the confidence interval you selected in problem 3 our conclusion is that:











(a) the current study does provide significant evidence that the mean number of weekly hours has changed over the past year since 8 falls outside the confidence interval.





(b) the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year since 8 falls outside the confidence interval.





(c) the current study does provide significant evidence that the mean number of weekly hours has changed over the past year since 8 falls inside the confidence interval.





(d) the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year since 8 falls inside the confidence interval.





(e) None of the above. The only way to reach a conclusion is by finding the p-value of the test.

Statistics Question?
ANSWER (d) the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year since 8 falls inside the confidence interval.








COMPUTATION AND METHODOLOGY





A PREDICTION INTERVAL FOR A SINGLE X VALUE





1. x-bar +/- (t-critical value) * s * SQRT[1 + 1/n]





x-bar SAMPLE AVERAGE [8.5]


s STANDARD DEVIATION [3.6]


n SAMPLE SIZE [81]





2. t-critical value "look-up" table [2.272]





x-bar +/- (t-critical value) * s * SQRT[1 + 1/n]


=8.5 +/- 2.272 * 3.6 *SQRT[1 +1/81] = [16.7 , 0.3]