A random sample of 40 12th-grade students was asked how long it took to get to school. The sample mean was 15.5 minutes and the sample standard deviation was 12.7 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). a. The 95% confidence interval is from minutes to minutes. (Round to two decimal places as needed. Use ascending order.) b. Would a 90% confidence interval based on this sample be wider or narrower than the 95% confidence interval? O 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. O 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. OC. The 95% interval is wider because it has a greater confidence level, and therefore uses a greater standard error, which creates a wider interval. O 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.)
A random sample of 40 12th-grade students was asked how long it took to get to school. The sample mean was 15.5 minutes and the sample standard deviation was 12.7 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). a. The 95% confidence interval is from minutes to minutes. (Round to two decimal places as needed. Use ascending order.) b. Would a 90% confidence interval based on this sample be wider or narrower than the 95% confidence interval? O 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. O 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. OC. The 95% interval is wider because it has a greater confidence level, and therefore uses a greater standard error, which creates a wider interval. O 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.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 1GP
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Transcribed Image Text:A random sample of 40 12th-grade students was asked how long it took to get to school. The sample mean was 15.5 minutes and the sample standard deviation was 12.7
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).
a. The 95% confidence interval is from minutes to minutes.
(Round to two decimal places as needed. Use ascending order.)
b. Would a 90% confidence interval based on this sample be wider or narrower than the 95% confidence interval?
O 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.
O 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.
O 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.
O 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.)
This interval is narrower than the interval in part a.
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