In a random sample of 88 people, the mean commute time to work was 36.536.5 minutes and the standard deviation was 7.47.4 minut
es. A 9898% confidence interval using the t-distribution was calculated to be (28.7 comma 44.3 )(28.7,44.3). After researching commute times to work, it was found that the population standard deviation is 8.68.6 minutes. Find the margin of error and construct a 9898% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.
The 98% confidence interval (34.36, 38.64) found by normal distribution with the appropriate calculations for a standard deviation that is known is narrower than the interval (28.7,44.3) found by the t-distribution (population standard deviation is unknown) .