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

Question

In a random sample of 8 people, the mean commute time to work was 33.5 minutes and the standard deviation was 7.2 minutes. A 90 % confidence interval using the t-distribution was calculated to be left parenthesis 28.7 comma 38.3 right parenthesis . After researching commute times to work, it was found that the population standard deviation is 9.1 minutes. Find the margin of error and construct a 90 % 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.)

A 90 % confidence interval using the standard normal distribution is (_____,_____) . (Round to one decimal place as needed.) Compare the results.

Choose the correct answer below.

A. The confidence interval found using the standard normal distribution has smaller lower and upper confidence interval limits.

B. The confidence interval found using the standard normal distribution is narrower than the confidence interval found using the student's t-distribution.

C. The confidence interval found using the standard normal distribution is the same as the confidence interval found using the student's t-distribution.

D. The confidence interval found using the standard normal distribution is wider than the confidence interval found using the student's t-distribution.

Explanation / Answer

Margin of Error mu=1.645*9.1/sqrt(8)=5.29

CI=[33.5-5.2925,33.5+5.2925]=[28.2,38.8]

The confidence interval found using the normal distribution is wider than the CI found using the t distribution

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