A teacher believes that students who study more than four hours for her tests will do better than students who do not study for her tests. To test this belief, the teacher recruited n=8 students. She had the n=8 students take one of her tests without studying. Without studying, the mean score on the test was M1=85, with a sample standard deviation of s1=5. Then the teacher had the same n=8 students take one of her tests after studying for four hours. After studying for four hours, the mean score on the test was M2=75, with a sample standard deviation of s2=4. The correlation between the 8 students' scores on the first test and the 8 students' scores on the second test was r = +.96. Perform a t-test between correlated samples by answering the questions below. Use an alpha-level of α=.05. 1. What is the research hypothesis, H1? 2. What is the null hypothesis, H0? 3. What is the degrees of freedom for this problem, df? 4. What is the critical value of t, tcrit? (Be sure to use a + or a - sign for your answer.) 5. What is the mean of the distribution of the difference between correlated sample means, μM1-M2? 6. What is the standard deviation of the distribution of the difference between correlated sample means, σM1-M2? 7. What is the z-score of the difference between sample means, M1-M2? 7. Based on the relation between the critical value of t and the t-score of the difference between sample means, can you reject the null hypothesis? 8. Based on whether or not you can reject the null hypothesis, can you accept the research hypothesis?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A teacher believes that students who study more than four hours for her tests will do better than students who do not study for her tests. To test this belief, the teacher recruited n=8 students. She had the n=8 students take one of her tests without studying. Without studying, the mean score on the test was M₁=85, with a sample standard deviation of s₁=5. Then the teacher had the same n=8 students take one of her tests after studying for four hours. After studying for four hours, the mean score on the test was M₂=75, with a sample standard deviation of s₂=4. The correlation between the 8 students' scores on the first test and the 8 students' scores on the second test was r = +.96.

Perform a t-test between correlated samples by answering the questions below. Use an alpha-level of α=.05.

1. What is the research hypothesis, H₁?

2. What is the null hypothesis, H₀?

3. What is the degrees of freedom for this problem, df?

4. What is the critical value of t, t_crit? (Be sure to use a + or a - sign for your answer.)

5. What is the mean of the distribution of the difference between correlated sample means, μ_M1-M2?

6. What is the standard deviation of the distribution of the difference between correlated sample means, σ_M1-M2?

7. What is the z-score of the difference between sample means, M₁-M₂?

7. Based on the relation between the critical value of t and the t-score of the difference between sample means, can you reject the null hypothesis?

8. Based on whether or not you can reject the null hypothesis, can you accept the research hypothesis?

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