Chapter 7, Problem 1P

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8th Edition

Frederick J Gravetter + 1 other

ISBN: 9781133956570

Textbook Problem

Describe the distribution of sample means (shape, expected value, and standard error) for samples of *n* = 100 selected from a population with a mean of μ = 40 and a standard deviation of σ = 10.

To determine

**To define:** The distribution of sample means.

Answer

The distribution of the sample mean is approximately normal with mean of

Explanation

**Given Info:**

The population mean is

**Calculation:**

Since, given sample size

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, sample means is equals to the population mean that is

If
*n* represents sample size. Then,

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

Substitute

So, standard error of distribution of sample means is

Thus, the shape, mean and standard error of the distribution of sample means are normal, 40 and 1 respectively.

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