   Chapter 7.5, Problem 4LC Essentials of Statistics for the B...

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

Solutions

Chapter
Section Essentials of Statistics for the B...

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

A sample of n = 16 individuals is selected from a normal population with a mean of μ = 50 with σ = 12. After a treatment is administered to the sample, the sample mean is found to be M = 57. Is this sample mean likely to occur if the treatment has no effect? Specifically, is the sample mean within the range of values that would be expected 95% of the time?

To determine

To find: The range of values for the sample mean would be expected 95% of the time and the sample mean is likely to occur if the treatment has no effect.

Explanation

Given info:

The sample of n=16 individuals is selected from a population with a mean of μ=50 and standard deviation of σ=12. The sample mean is M=57.

Calculation:

The formula for calculating the z-score is,

z=MμσM

Where, σM=σn

The standard error is,

σM=1216=3

The range of values for the sample mean would be expected 95% of the time is,

For z=1

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