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 = .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.
To find: Whether or not the treatment has significant effect on performance at .
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 is performed.
Step 1: Null Hypothesis is and Alternate Hypothesis is
Step 2: For a sample of , the t-statistics will have degrees of freedom, i.e. . For a one-tailed test with and , the critical value (CV) is obtained from the t-table as
Step 3: t-statistics can be calculated using formula:
First, calculate sample standard deviation, s, using formula:
Substitute and in the formula
To find: Cohen’s d and
To make: The 90% confidence interval estimate for the given question
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