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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 normal distribution has a mean of μ = 60 and a standard deviation of σ = 18. For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size.

a. M = 67 for n = 4 scores

b.    M = 67 for n = 36 scores

a.

To determine

To find: The z-score for the sample mean.

To determine: Sample mean is a typical, representative value or an extreme value.

Explanation

Given info:

The population mean is μ=60, the standard deviation is σ=18, the sample mean is M=67 and the sample size is n=4.

Calculation:

If μ and σ represents the population mean and standard deviation respectively. Let n represents numbers of scores in each sample. Let M represents sample mean. Then, z-score is given by:

z=(Mμ)σn

Consider μ=60, σ=18, n=4 and M=67

b.

To determine

To find: The z-score for the sample mean.

To determine: Sample mean is a typical, representative value or an extreme value.

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