Chapter 7, Problem 2P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

A sample is selected from a population with a mean μ = 40 and a standard deviation of σ = 8.

**a.**If the sample has*n =*4 scores, what is the expected value of*M*and the standard error of*M*?**b.**If the sample has*n =*16 scores, what is the expected value of*M*and the standard error of*M*?

**a.**

To determine

**To find:** The expected value and standard error of *M*.

Explanation

**Given Info:**

The population mean is

**Calculation:**

Since expected value of the mean of the distribution of sample means is the average of all the possible samples means. The sample means are the representative of the population mean from which samples have been drawn. The average of all possible samples takes all population units into the consideration. Therefore, average of all sample means will be equal to population mean. Hence, expected value of *M* is equals to the population mean that is 40.

If
*n* represents sample size. Then,

Standard error measures the distance expected on an average between *M* and

**b.**

To determine

**To find:** The expected value and standard error of *M*.

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