Answered: Suppose a random sample of size 49 is… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 2GP

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**Standard Error of the Mean Calculation**

Suppose a random sample of size 49 is selected from a population with a standard deviation (\(\sigma\)) of 11. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

**a. The population size is infinite (to 2 decimals).**
- Standard Error: 1.57

**b. The population size is \(N = 50{,}000\) (to 2 decimals).**
- Standard Error: 1.57

**c. The population size is \(N = 5{,}000\) (to 2 decimals).**
- Standard Error: 1.56

**d. The population size is \(N = 500\) (to 2 decimals).**
- Standard Error: [Not provided]

The standard error is calculated using the formula:

\[
SE = \frac{\sigma}{\sqrt{n}}
\]

Where \(SE\) is the standard error, \(\sigma\) is the population standard deviation, and \(n\) is the sample size. When the population is finite, the finite population correction (FPC) factor is applied:

\[
SE_{finite} = SE \times \sqrt{\frac{N-n}{N-1}}
\]

Where \(N\) is the population size.

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