Answered: teacher believes that students who…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 27PPS

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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 16 students and randomly assigned them to two groups: G₁: a group of n₁=8 students that studied more than four hours for her test, and G₂: a group of n₂=8 students that did not study for her test.

The following are the data from G1, who studied more than four hours for the test:

n₁=8

M₁=85

s₁=5 (this is the standard deviation of the sample, dividing the sum of squares by n₁)

The following are the data from G2, who did not study for the test:

n₂=8

M₂=75

s₂=4 (this is the standard deviation of the sample, dividing the sum of squares by n₂)

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

0. Using formulas from Section 4, compute the estimates of the population variances, est. σ₁² and est. σ₂² (from s₁ and s₂ above).

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 independent sample means, μ_M1-M2?

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

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

8. 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?

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

Show your work for all problems.

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