In a random sample of 26 people, the mean commute time to work was 33.7 minutes

Question

In a random sample of 26 people, the mean commute time to work was 33.7 minutes and the standard deviation was 7.3 minutes. Assume the population is normally 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 results. 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 population mean commute time is between the bounds of the confidence interval. B. With 98% confidence, it can be said that the commute time is between the bounds of the confidence interval. C. It can be said that 98% of people have a commute time between the bounds of the confidence interval. D. If a large sample of people are taken approximately 98% of them will have commute times between the bounds of the confidence interval.

Explanation / Answer

The statistical software output for this problem is:

One sample T confidence interval:
: Mean of population

98% confidence interval results:

Hence,

Confidence interval: (30.1, 37.3)

Margin of error = (37.3 - 30.1) / 2 = 7.2 / 2 = 3.6

Interpretation: Option A is correct.

Mean Sample Mean Std. Err. DF L. Limit U. Limit 33.7 1.4316478 25 30.142202 37.257798

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