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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 plans to conduct an experiment evalu­ating the effect of a treatment. A sample of n = 9 participants is selected and each person receives the treatment before being tested on a standardized dex­terity task. The treatment is expected to lower scores on the test by an average of 30 points. For the regular population, scores on the dexterity task form a normal distribution with μ = 240 and σ = 30.

a. If the researcher uses a two-tailed test with α – .05, what is the power of the hypothesis test?

b. Again assuming a two-tailed test with α – .05, what is the power of the hypothesis test if the sample size is increased to n = 25?

a.

To determine
The power of the test if the researcher uses a sample of n=9 .

Explanation

Given info:

Population mean before treatment is given as 240, Population mean after treatment is given as 210, standard deviation is given as 30, alpha level is given as 0.05 and sample size is given as 9.

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=309=303=10

Now X value before treatment is calculated as:

Z=Xμσm1.96=X24010X=1

b.

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

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