Question

1. Suppose that an accounting firm does a study to determine the time needed to complete one person’s tax forms. It randomly selects 100 people. The sample mean is 23.6 hours. There is a known population standard deviation of 7.0 hours. The population distribution is assumed to be normal.

A. Find the margin of error associated with a 95% confidence interval.

B. Find and interpret the 95% confidence interval for the mean amount of time to complete a person’s tax form.

C. What effect does in increase in sample size have on the margin of error?

Answer 1

Solution:

We are given:

A. The margin of error associated with a 95% confidence interval is:

Where:

is the critical value at the 0.05 significance level.

  

B. The 95% confidence interval for the mean of time to complete a person's tax form is:

There is a 95% chance that the confidence interval calculated contains the true population mean amount of time to complete a person’s tax form.

C. The increase in sample size will reduce the margin of error.