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Essentials of Statistics for the B...

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

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

A random simple is selected from a normal population with a mean of μ = 30 and a standard deviation of σ = 8. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 33.

a. If the sample consists of n = 16 scores, 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 sample consists of n = 64 scores, is the sample mean sufficient effect? Use a two-tailed test with α = .05.

c. Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.

a.

To determine
Whether the sample mean is sufficient to conclude that the treatment has a significant effect, when n is 16.

Explanation

Given info:

Samples mean (M) is 33, population mean is 30, standard deviation is 8, alpha level is 0.05 and sample size is 16.

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 30 and two tailed test is used, so the null hypothesis and alternative hypothesis for this question are:

H0:μ=30H1:μ30

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
Whether the sample mean is sufficient to conclude that the treatment has a significant effect, when n is 64.

c.

To determine

To explain: The size of the sample influences the outcome of a hypothesis test.

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