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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 researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of μ = 80 and a standard deviation of σ = 20. The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with α = .05.

a. Compute the power of the test if the researcher uses a sample of n = 16 individuals.

b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.

a.

To determine
The power of the test if the researcher uses a sample of n=16.

Explanation

Given info:

Population mean before treatment is 80, Population mean after treatment is 92, standard deviation is 20, alpha level is 0.05 and sample size is 16.

Calculation:

As alpha level is given so before treatment z-score value is calculated as 1.96 using z table. Standard error ( σm) calculated as:

σm=σn=2016=204=5

Now X value before treatment is calculated as:

Z=Xμσm1.96=X805X=1

b.

To determine
The power of the test if the researcher uses a sample of n=25.

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