Question

In a random sample of 8 people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.2 minutes. A 95% confidence interval using the t-distribution was calculated to be left parenthesis 29.5 comma 41.5 right parenthesis. 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 95% 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:___

Answer #1

Given that, sample size ( n ) = 8

sample mean = 35.5 minutes

population standard deviation = 9.2

A 95% confidence level has significance level = 0.05 and critical value is,

Margin of error of is,

The margin of error of is
**6.4**

And 95% confidenc interval for is,

The 95% confidence jnterval is, **(29.1,
41.9)**

The confidence interval found using the standard normal distribution is wider than the confidence interval found using the students t-distribution.

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