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Essentials of Statistics for the B...

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

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

A sample of n = 40 is selected from a normal population with μ = 75 msec. and σ = 12, and a treatment is administered to the sample, The treatment is expected to increase scores by an average of 4 msec.

a. If the treatment effect is evaluated with a two-tailed hypothesis test using α = .05, what is the power of the test?

b. What is the power of the test if the researcher uses a one-tailed test with α = .05?

a.

To determine

To find: The power of the test if the treatment effect is evaluated with a two-tailed hypothesis test using α=0.05

Explanation

Given info:

n=40, μ=75msec, σ=12 and α=0.05.

Calculation:

Two tailed test

In case when treatment has no effect and the population mean is μ=75msec

When treatment adds to each person’s score by 4 msec, the sample mean are centred around μ=75msec.

Both distribution have standard error (σM)

σM=σn=1240=1.8971.90

At α=0.05, the critical boundaries comes out to be Z=1.96 or Z=1.96.

For the distribution on the left hand side, the critical boundary of Z=±1.96 corresponds to a location that is above μ=75 by distance equals to

1

b.

To determine

To find: The power of the test if the treatment effect is evaluated with a one-tailed hypothesis test using α=0.05

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