Question

The weekly time spent​ (in hours) on homework for 18 randomly selected high school students is given below. Use technology to construct​ 90%, 95%, and​ 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. Assume the weekly time spent on homework is normally distributed. 13.113.1 12.112.1 14.714.7 15.215.2 8.68.6 10.710.7 11.811.8 8.58.5 9.99.9 9.69.6 11.111.1 11.911.9 15.915.9 11.911.9 12.212.2 11.511.5 13.513.5 12.212.2 The lower limit of the​ 90% confidence interval is 11.0611.06​, and the upper limit is 12.7612.76. ​(Round to two decimal places as​ needed.) The lower limit of the​ 95% confidence interval is 10.8810.88​, and the upper limit is 12.9412.94. ​(Round to two decimal places as​ needed.) The lower limit of the​ 99% confidence interval is 10.5010.50​, and the upper limit is 13.3313.33. ​(Round to two decimal places as​ needed.) Interpret the​ 90% confidence interval. With nothing​% ​confidence, one can say that the ▼ population sample mean time spent on homework is between nothing and nothing hours. ​(Round to two decimal places as​ needed.)

Answer 1

Solution:

Assume the weekly time spent on homework is normally distributed. 13.113.1 12.112.1 14.714.7 15.215.2 8.68.6 10.710.7 11.811.8 8.58.5 9.99.9 9.69.6 11.111.1 11.911.9 15.915.9 11.911.9 12.212.2 11.511.5 13.513.5 12.212.2 The lower limit of the​ 90% confidence interval is 11.06​, and the upper limit is 12.76. ​(Round to two decimal places as​ needed.) The lower limit of the​ 95% confidence interval is 10.88​, and the upper limit is 12.94. ​(Round to two decimal places as​ needed.) The lower limit of the​ 99% confidence interval is 10.50​, and the upper limit is 13.33. ​(Round to two decimal places as​ needed.)

We have to Interpret the​ 90% confidence interval.

With 90​% ​confidence, one can say that the population sample mean time spent on homework is between 11.06 and 12.76 hours.

The interpretation for 95% will be the following:

With 95% confidence, one can say that the population sample mean time spent on homework is between 10.88 and 12.94 hours.

The interpretation for 99% will be the following:

With 99% confidence, one can say that the population sample mean time spent on homework is between 10.50 and 13.33 hours.