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.)
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5 and sample size = 40 Standard error = 12.5 / sqrt(40) = 1.98 ** Show more…
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