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.

IQ of statistics professors You want to estimate $\sigma$for the population of IQ scores of statistics professors. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 1% of $\sigma$. Is this sample size practical?

Short answer

The value of the minimum sample size to be 95% confident that the sample standard deviation is within 1% of the value of the population standard deviation $\left(\sigma \right)$is equal to 19205.

Since the sample size is very large, it is not practically possible to consider such a large sample to estimate the standard deviation of the IQ scores of professors.

Step-by-step solution

Given information 

It is given that there should be 95% confidence that the sample standard deviation should be within 1% of the value of the population standard deviation. The sample size is needed to be determined.

Determine the sample size

Using the table given in the book, the minimum sample size required to be 95% confident that the sample standard deviation should be within 1% of the value of the population standard deviation is equal to 19205.

Therefore, the required sample size is equal to 19205.

Step 3:Practicality of the sample size 

A sample size of 19205 is extremely large, and it is not humanly possible to consider such a large sample. Moreover, there won’t be 19205 readily available professors for the sample.

Thus, the sample size of 19205 is quite impractical.