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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 investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systolic scores average μ = 160 with a standard deviation of σ = 20, and the scores form a normal-shaped distribution. The researcher plans to select a sample of n = 25 individuals, and measure their systolic blood pressure after they take the medication for 60 days. If the researcher uses a two-tailed test with α = .05.

a. What is the power of the test if the medication has a 5-point effect?

b. What is the power of the test if the medications has a 10-points effect?

a.

To determine
The power of the test if the researcher uses a two-tailed hypothesis test with 5 point medication effect.

Explanation

Given info:

The systolic scores average μ=160. The standard deviation σ=20. The researcher took a sample of size 25 and measured their systolic blood pressure after using a medicine for 60 days. Here the medication has 5point effect.

Calculation:

As alpha level is given and two-tailed hypothesis test is used then before treatment z-score value is calculated as 1.96 using z table. Standard error ( σm) calculated as:

Standard error:

σm=σn=2025=205=4

Now X value before treatment is calculated as:

Z=Xμσm1

b.

To determine
The power of the test if the researcher uses a two-tailed hypothesis test with 10 point medication effect

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