In a random sample of 18 people, the mean commute time to work was 32.2 minutes

Question

In a random sample of 18 people, the mean commute time to work was 32.2 minutes and the standard deviation was 7.1 minutes. Assume the distributed and use a t-distribution to construct a 98% confidence interval for the population mean mu. What is the margin of error of mu? Interpret The confidence interval for the population mean mu is (Round to one decimal place as needed.) The margin of error of mu is (Round to one decimal place as needed.) Interpret the results A. With 98% confidence, it can be said that the commute time is between the bounds of the confidence interval. B. With 98% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval. C. If a large sample of people are taken approximately 98% of them will have commute times between the bounds of the confidence interval. D. It can be said that 98% of people have a commute time between the bounds of the confidence interval.

Explanation / Answer

For a t-distribution with n=18 and 98% confidence level,it given df=18-1=17& t-statistic is now calculated as 2.567 from t tables.

Hence margin of error = t* Sigma/sqrt(n) = 2.567*7.1/sqrt(18) = 4.29

Hence,confidence interval is (32.2-4.29,32.2+4.29) = (27.904,36.495)

The correct answer is D from the definition of confidence interval

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