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

For Study (a), we are dealing with a one-tailed test with a high predicted mean difference. In this case, we are testing if the mean difference in the first population is greater than the mean difference in the second population (which is assumed to be 0). Therefore, the research hypothesis is testing for a positive difference.

The correct research hypothesis for Study (a) is:

A. The mean difference for the first population is greater than the mean difference for the second population.

If you need help with the calculations for the t-test or effect size, feel free to ask!

Would you like details on calculating the t-test for dependent means or estimating the effect size? Here are 5 questions that relate to what we've just discussed:

  1. How do we calculate a t-test for dependent means in a study like this?
  2. What is the process for estimating the effect size (Cohen's d) for dependent samples?
  3. What does the significance level of 0.05 imply for this test?
  4. Why is the mean difference for the second population assumed to be 0?
  5. How do we interpret the directionality in one-tailed versus two-tailed tests?

Tip: For dependent samples t-tests, the key is the difference between scores before and after a treatment or condition. Always calculate the mean of these difference scores first!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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

Related Recommendation

Independent Samples t-Test Example: Comparing Two Teaching Methods

Hypothesis Testing: One-Sample t-test for Population Mean

How to Find the Test Statistic for a Two-Sample t-Test

Simplified One-Sample t-Test Calculation with Step-by-Step Example

How to Perform a Two-Tailed T-Test for the Mean of a Sample