In a random sample of 8 people, the mean commute time to work was 35.5 minutes a

Question

In a random sample of 8 people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.4 minutes. A 98% confidence interval using the t-distribution was calculated to be (27.7, 43 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. The margin of error of mu is (Round to two decimal places as needed.)

Explanation / Answer

n = 8     

x-bar = 35.5     

s = 8.9     

% = 98     

Standard Error, SE = /n =    8.9 /8 = 3.146625176

z- score = 2.326347874     

Margin of error = z * SE =     2.32634787404085 * 3.14662517628014 = 7.320144789

Lower Limit of the confidence interval = x-bar - Margin of error =      35.5 - 7.32014478924271 = 28.17985521

Upper Limit of the confidence interval = x-bar + Margin of error =      35.5 + 7.32014478924271 = 42.82014479

The 98% confidence interval is [28.18, 42.82]

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