   Chapter 8, Problem 7P 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 random sample of n = 25 scores is selected from a normal population with a mean of μ = 40. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 44.a. If the population standard deviation is σ = 5, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.b. If the population standard deviation is σ = 15, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05.c. Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

a.

To determine
The sample mean sufficient to conclude that the treatment has a significant effect if the population standard deviation is σ=5.

Explanation

Given info:

Samples mean (M) is 44, population mean is 40, standard deviation is 5, alpha level is 0.05 and sample size is 25.

Justification:

The null hypothesis states that there is no effect of the treatment and alternative hypothesis states opposite of null hypothesis. As given in the question that population mean is 40 and two tailed test is used, so the null hypothesis and alternative hypothesis for this question are:

H0:μ=40H1:μ40

The alpha level is given in the question as 0.05 and need to find boundaries of the critical region. As given in the question that two tailed hypothesis test used, so acceptance region is:

p=1α2=10.052=10.025=0.975

The z-score critical value at 0.975 or at α=0.05 is ±1.96 using the z table

b.

To determine
The sample mean sufficient to conclude that the treatment has a significant effect if the population standard deviation is σ=15.

c.

To determine

To explain: The change in magnitude of the standard deviation influences the outcome of a hypothesis test.

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