Question

Addicted to the Internet?

The Ann Arbor public school officials would like to estimate the population mean daily Internet usage time for all Ann Arbor teens. To do so, a large random sample of Ann Arbor teens was selected. Here are the results of their study.

The 95% confidence interval for the mean daily internet usage time for the population of all such Ann Arbor teens was found to be (6.7 hours, 9.3 hours).

The 99% confidence interval or the mean daily internet usage time for the population of all such Ann Arbor teens was found to be (6.257 hours, 9.743 hours).

The Ann Arbor public school officials know that you have some statistical background and would like your opinion. Please read each statement carefully and share with us your opinion.

Answer 1

In my opinion, the 99% confidence interval will be more accurate.

Explanation:

Statisticians define a confidence interval (CI) as a type of estimate computed from the statistics of the observed data. The Ann Arbor Public school's official are sure to some extent the their students spend considerable period of time on internet.

Using the 95% confidence interval, they estimated to true mean of the hours spend on internet daily by the teens is 95% certain to fall between [6.7Hours, 9.3Hours].

Again by Using the 95% confidence interval, they estimated to true mean of the hours spend on internet daily by the teens is 99% certain to fall between [6.257Hours, 9.743Hours].

In my opinion, the choice of using 95% and 99% confidence interval is to arrive at more accurate mean of hours spend on internet daily by Ann Arbor public school teens. 99% confidence interval is more wider and accurate considering the large random sample selection.

Answer 2

Increasing the confidence level from 95% to 99% increases the margin of error which in turn decreased the lower limit and increased the upper limit of the 99% confidence interval.

Explanation:

95% confidence interval is (6.7 hours, 9.3 hours)

Margin of error = (9.3-6.7)/2 = 1.3 hours

99% confidence interval is (6.257 hours, 9.743 hours)

Margin of error = (9.743-6.257)/2 = 1.743 hours

The margin of error increased because as the confidence level increases, the critical value (t) also increases.

Increasing the margin of error invariably would decrease the lower limit of the mean and increase the upper limit.