In a random sample of 20 people, the mean commute time to work was 32.5 minutes

Question

In a random sample of 20 people, the mean commute time to work was 32.5 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 90% 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 () The margin of error of mu is. Interpret the results A. With 90% confidence, it can be said that the commute time is between the bounds of the confidence interval. B. If a large sample of people are taken approximately 90% of them will have commute times between the bounds of the confidence interval. C. It can be said that 90% of people have a commute time between the bounds of the confidence interval. D. With 90% confidence, it can be said that the population mean commute time is 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

90% confidence interval results:

Hence,

90% confidence interval will be:

(29.8, 35.2)

Margin of error = (35.2 - 29.8) / 2 = 2.7

Option D is correct.

Mean Sample Mean Std. Err. DF L. Limit U. Limit 32.5 1.5876083 19 29.754814 35.245186

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