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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 effect of a treatment by measuring performance for a sample of n = 9 participants before and after they receive the treatment. For this sample, performance scores increased after treatment by an average of M = 1.9 points with SS = 200.

a. Are the data sufficient to conclude that treatment has a significant effect on performance? Use a two-tailed test with α = .05.

b. Compute the effect size for the treatment using both Cohen’s d and r2.

c. Compute the 90% confidence for the population mean difference.

a.

To determine

To find: Whether or not the treatment has significant effect on performance at α=0.05.

Explanation

Given info:

A sample of 9 individuals is selected from a population. The sample mean and sum of squared difference (SS) is found to be 1.9 and 200 respectively. Two-tailed hypothesis test using α=0.05 is performed.

Calculations:

Step 1: Null Hypothesis is H0:μD=0 and Alternate Hypothesis is H1:μD0

Step 2: For a sample of n=9, the t-statistics will have (n1) degrees of freedom, i.e. df=8. For a one-tailed test with α=0.05 and df=8, the critical value (CV) is obtained from the t-table as t=±2.306

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

t=Mμsm

First, calculate sample standard deviation, s, using formula:

s=SSn1

Substitute SS=200 and n=9 in the formula

s=20091=2008=25

b.

To determine

To find: Cohen’s d and r2

c.

To determine

To make: The 90% confidence interval estimate for the given question

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