In a random sample of 8 8 people, the mean commute time to work was 33.5 33.5 mi

Question

In a random sample of 8 8 people, the mean commute time to work was 33.5 33.5 minutes and the standard deviation was 7.4 7.4 minutes. A 90 90% confidence interval using the t-distribution was calculated to be left parenthesis 28.5 comma 38.5 right parenthesis (28.5,38.5). After researching commute times to work, it was found that the population standard deviation is 9.6 9.6 minutes. Find the margin of error and construct a 90 90% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

Explanation / Answer

Ans:

population standard deviation=9.6

sample mean=33.5

n=8

90% confidence interval for mean

=33.5+/-1.645*(9.6/sqrt(8))

=33.5+/-5.6

=(27.9, 39.1)

This confidence interval is wider than t interval,as population standard deviation is larger.

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