Question

In a random sample of five ​people, the mean driving distance to work was 24.9 miles and the standard deviation was 4.3 miles. Assuming the population is normally distributed and using the​ t-distribution, a 99​%confidence interval for the population mean mu is left parenthesis 16.0 comma 33.8 right parenthesis ​(and the margin of error is 8.9​). Through​ research, it has been found that the population standard deviation of driving distances to work is 3.3 Using the standard normal distribution with the appropriate calculations for a standard deviation that is​ known, find the margin of error and construct a 99%confidence interval for the population mean mu. Interpret and compare the results.

Identify the margin of error =?

Construct a 99% confidence interval for population mean. (?, ?)

Answer 1

margin of error E = Z * / sqrt(n)

= 2.576 * 3.3 / sqrt(5)

= 3.80

99% Confidence interval for is

- E < < + E

24.9 - 3.80 < < 24.9 + 3.80

21.1 < < 28.7

99% CI is ( 21.1 , 28.7 )