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.