Estimation 8 Copyright Cengage Learning All rights reserved

Estimation 8 Copyright © Cengage Learning. All rights reserved.

Using technology to find a confidence interval 2

Sample Size for Estimating the Mean 3

Sample Size for Estimating the Mean In the design stages of statistical research projects, it is a good idea to decide in advance on the confidence level you wish to use and to select the maximal margin of error E you want for your project. How you choose to make these decisions depends on the requirements of the project and the practical nature of the problem. Whatever specifications you make, the next step is to determine the sample size. Solving the formula that gives the maximal margin of error E for n enables us to determine the minimal sample size. 4

Sample Size for Estimating the Mean Procedure: 5

Example 3 – Sample size for estimating A wildlife study is designed to find the mean weight of salmon caught by an Alaskan fishing company. A preliminary study of a random sample of 50 salmon showed s 2. 15 pounds. How large a sample should be taken to be 99% confident that the sample mean x is within 0. 20 pound of the true mean weight ? 6

Example 3 – Solution cont’d In this problem, z 0. 99 = 2. 575 (see Table 8 -2) and E = 0. 20. The preliminary study of 50 fish is large enough to permit a good approximation of by s = 2. 15. Therefore, Equation (10) becomes 7

Example 3 – Solution cont’d Note: In determining sample size, any fractional value of n is always rounded to the next higher whole number. We conclude that a sample size of 767 will be large enough to satisfy the specifications. Of course, a sample size larger than 767 also works. 8