In a random sample of 8 ​people, the mean commute time to work was 34.5 minutes and the standard deviation was 7.4 minutes. A 98​% confidence interval using the​ t-distribution was calculated to be (26.7,42.3). After researching commute times to​ work, it was found that the population standard deviation is 8.9 minutes. Find the margin of error and construct a 98​% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

In a random sample of

8

​people, the mean commute time to work was

34.5

minutes and the standard deviation was

7.4

minutes. A

98​%

confidence interval using the​ t-distribution was calculated to be

(26.7,42.3).

After researching commute times to​ work, it was found that the population standard deviation is

8.9

minutes. Find the margin of error and construct a

98​%

confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

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