Math Problem Statement
In each of the studies in the accompanying table using difference scores, test the significance using a t test for dependent means. Include an estimate of effect size and whether it is considered approximately small, medium, or large. Study Number of Difference Scores in Sample Mean of Difference Scores in Sample Estimated Population Variance of Difference Scores Tails Significance Level (a) 20 1.30 8.03 1 (high predicted) 0.05 (b) 164 2.60 414.02 2 0.05 (c) 15 negative 2.40 4.38 1 (low predicted) 0.01 pop-up content ends
Click here to view Cutoff Scores for the t Distribution.LOADING... Question content area bottom Part 1 For Study (a), let the first population be the one from which the sample is taken and let the second population be the one whose mean difference is 0. What is the research hypothesis for this test? Choose the correct answer below. A. The mean difference for the first population is greater than the mean difference for the second population. B. The mean difference for the first population is different from the mean difference for the second population. C. The mean difference for the first population is the same as the mean difference for the second population. D. The mean difference for the first population is less than the mean difference for the second population.
Solution
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Math Problem Analysis
Mathematical Concepts
T-test for dependent means
Effect size estimation
Statistical significance
One-tailed and two-tailed tests
Hypothesis testing
Formulas
t = (M - μ) / (S / √N)
Effect size (Cohen's d) = (M - μ) / SD
Theorems
Central Limit Theorem
Student's t-distribution
Suitable Grade Level
Undergraduate Statistics or Research Methods
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