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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

To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 35.

a. If the sample variance is s2 = 32, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?

b. If the sample variance is s2 = 72, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?

c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?

a.

To determine

To Find: Whether or not to conclude that the treatment has a significant effect for the given question using two-tailed test with α=0.05 and s2=32.

Explanation

Given info:

A sample of 8 individual is selected from a population with mean 40. The sample mean is 35 and variance, s2=32. A two-tailed hypothesis test using α=0.05 is to be performed.

Calculation:

Step 1: Null Hypothesis is H0:μ=40 and Alternate Hypothesis is H1:μ40

Step 2: For a sample of n=8, the t-statistics will have (n1) degrees of freedom, i.e. df=7. For a two-tailed test with α=0.05 and df=7, the critical value (CV)  is obtained from the t-table as t=±2.3646.

Step 3: The t-statistics can be calculated using formula:

t=Mμsm

Calculate sm using the formula:

sm=s2n=328</

b.

To determine

To Find: Whether or not to conclude that the treatment has a significant effect for the given question using two-tailed test with α=0.05 and s2=72.

c.

To determine

To State : How does the variability of the scores in sample influence the outcome of a hypothesis test.

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