Question

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

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 9.3 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.)

Solution :

Given that, = 9.3

n = 8

A ) At 90% confidence level the z is , = 1 - 90% = 1 - 0.90 = 0.10 / 2 = 0.10 / 2 = 0.05

Z /2 = Z0.05 = 1.645

Margin of error = E = Z /2* (  /n)

= 1.645 * (9.3 / 8 ) = 5.41

The margin of error of mu is =5.41

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