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.

Space mountain You want to estimate $\sigma$for the population of waiting times for the space mountain ride in Walt Disney World. You want to be 99% confident that the sample standard deviation is within 1% of$\sigma$. Find the minimum sample size. Is this sample size practical?

Short answer

The value of the minimum sample size to be 99% confident that the sample standard deviation is within 1% of the value of the population standard deviation $\left(\sigma \right)$is equal to 33218.

Since the sample size is enormous, it is not practically possible to consider such a large sample to estimate the standard deviation of the waiting times for the space mountain ride.

Step-by-step solution

Given information

It is given that there should be 99% 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 99% 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 33218.

Step 3:Practicality of the sample size 

A sample of size 33218 is huge. It is not feasible to consider such a large sample.

Thus, the sample size of 33218 is quite impractical.