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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

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.

  1. a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M?
  2. 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 μ=40, the standard deviation is σ=8 and the sample size is n=4.

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 μ and σ represents the population mean and standard deviation respectively. Let n represents sample size. Then,

μ=40σ=8n=4

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

b.

To determine

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

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