Question

Determining Sample Size. In Exercises 19–22, assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 7-2 on page 338 to find the indicated sample size. Quarters When setting specifications of quarters to be accepted in a vending machine, you must estimate the standard deviation of the population of quarters in use. Find the minimum sample size needed to be 99% confident that the sample standard deviation is within 10% of the population standard deviation.

Short answer

The minimum sample size needed is 336.

Step-by-step solution

Given information

The simple random samples are known to be selected from a normally distributed population.

The required level of confidence is 99%, and the sample standard deviation is within 10% of the population standard deviation.

Determination of the sample size

Refer to table 7-2 on page 338 for the sample size.

A portion of the table is shown below.

To be 99% confident that s is within	The minimum sample size
1%	33218
5%	1336
10%	336
20%	85
30%	38
40%	22
50%	14

In the table, for the 99% confidence level, refer to the second part of the table.

For the 10% deviation of the sample standard deviation from the population measure, look for 10% in the rows.

So, the corresponding measure of the sample size is 336.

The approximate computation of the sample size can also be carried out using the formula that involves the measurement of the margin of error.