A random sample of 40 12th-grade students was asked how long it took to get to school. The sample mean was 15.9 minutes and the sample standard deviation was 12.5 minutes.
a. Find a 95% confidence interval for the population mean time it takes 12th-grade students to get to school.
b. Would a 90% confidence interval based on this sample data be wider or narrower than the 95% confidence interval? Explain. Check your answer by constructing a 90% confidence interval and comparing the width of the interval with the width of the 95% confidence interval you found in part (a).
b. Would a 90% confidence interval based on this sample be wider or narrower than the 95% confidence interval?
A. The 90% interval is wider because it has a lower confidence level, and therefore uses a smaller critical value, which creates a wider interval.
B. The 90% interval is wider because it has a lower confidence level, and therefore uses a greater standard error, which creates a wider interval.
C. The 95% interval is wider because it has a greater confidence level, and therefore uses a greater standard error, which creates a wider interval.
D. The 95% interval is wider because it has a greater confidence level, and therefore uses a larger critical value, which creates a wider interval.
Check your answer by constructing a 90% confidence interval and comparing the width of the interval with the width of the 95% confidence interval you found in part (a).
The 90% confidence interval is from [ ] minutes to [ ] minutes.
(Round to two decimal places as needed. Use ascending order.)
