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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 sample of n = 16 scores is obtained from a population with a mean of μ = 45. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 49.2.

a. Assuming that the sample standard deviation is s = 8. compute r2 and the estimated Cohen's d to measure the sue of the treatment effect.

b. Assuming that the sample standard deviation is s = 20, compute r2 and the r2 estimated Cohen's d to measure the size of the treatment effect.

c. Comparing your answers from parts a and b, how does the variability of the scores in the sample influence the measures of effect size?

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 s=8

Explanation

Given info:

A sample of 16 individual is selected from a population with mean 45. The sample mean is 49.2 and standard deviation, s=8. A two-tailed hypothesis test using α=0.05 is to be performed.

Calculation:

Step 1: Null Hypothesis is H0:μ=45 and Alternate Hypothesis is H1:μ45

Step 2: For a sample of n=16, the t-statistics will have (n1) degrees of freedom, i.e. df=15. For a two-tailed test with α=0.05 and df=15, the critical value (CV) is obtained from the t-table as t=±2.1315

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

t=Mμsm

Calculate sm using the formula:

sm=s2n=(8)216=4=2

Now, substitute 49.2 for M, 45 for μ and 2 for sm in the formula

t=49.2452=4.22=2.1

Step 4: Rejection rule: Reject when tstatistics<2.1315 or tstatistics>2

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 s=20

c.

To determine

To State : What is the impact of sample size on the outcome of a hypothesis test and on the measure of effective size.

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