In a random sample of 8 ​people, the mean commute time to work was 33.5 minutes and the standard deviation was 7.3 minutes. A 90  % confidence interval using the​ t-distribution was calculated to be (28.6 comma 38.4).After researching commute times to​ work, it was found that the population standard deviation is 9.2 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.

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Author:Amos Gilat
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In a random sample of 8 ​people, the mean commute time to work was 33.5 minutes and the standard deviation was 7.3 minutes. A 90  % confidence interval using the​ t-distribution was calculated to be (28.6 comma 38.4).After researching commute times to​ work, it was found that the population standard deviation is 9.2 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.

 

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Step 1

Given,

X = 33.5Incorrect s =7.390% CI ( t-distribution) : (28.6,38.4)Correct σ = 9.2n = 8

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