Suppose you have the following pre-test and post-test scores for a random sample of five students. Student 1 2 3 4 5 Pre-test 63 73 54 56 52 Post-test 94 95 86 84 97 We would like to test the hypotheses Ho: H, = 0 verses H: H. > 0, where u, = the mean difference in pre-test and post-test scores for all students (post - pre). (a) We would like to carry out at test for the population mean difference. Calculate the point estimate. (b) If the null hypothesis is true, the t test statistic follows at distribution. How many degrees of freedom does it have? (c) Suppose the P-value of this test turned out to be less than 0.001. Which of the following is the correct conclusion? Use a = 0.05. O we have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post – pre) is less than zero. O we have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post – pre) is greater than zero. O we do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is less than zero. O we do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is greater than zero.
Suppose you have the following pre-test and post-test scores for a random sample of five students. Student 1 2 3 4 5 Pre-test 63 73 54 56 52 Post-test 94 95 86 84 97 We would like to test the hypotheses Ho: H, = 0 verses H: H. > 0, where u, = the mean difference in pre-test and post-test scores for all students (post - pre). (a) We would like to carry out at test for the population mean difference. Calculate the point estimate. (b) If the null hypothesis is true, the t test statistic follows at distribution. How many degrees of freedom does it have? (c) Suppose the P-value of this test turned out to be less than 0.001. Which of the following is the correct conclusion? Use a = 0.05. O we have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post – pre) is less than zero. O we have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post – pre) is greater than zero. O we do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is less than zero. O we do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is greater than zero.
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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![Suppose you have the following pre-test and post-test scores for a random sample of five students.
| Student | 1 | 2 | 3 | 4 | 5 |
|---------|----|----|----|----|----|
| Pre-test | 63 | 73 | 54 | 56 | 52 |
| Post-test| 94 | 95 | 86 | 84 | 97 |
We would like to test the hypotheses \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d > 0 \), where \( \mu_d \) is the mean difference in pre-test and post-test scores for all students (post - pre).
*(a) We would like to carry out a t test for the population mean difference. Calculate the point estimate.*
[Text box]
*(b) If the null hypothesis is true, the t test statistic follows a t distribution. How many degrees of freedom does it have?*
[Text box]
*(c) Suppose the p-value of this test turned out to be less than 0.001. Which of the following is the correct conclusion? Use \(\alpha = 0.05\).*
- ○ We have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is less than zero.
- ○ We have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is greater than zero.
- ○ We do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is less than zero.
- ○ We do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is greater than zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a338546-f60c-4169-9d4b-257d05088060%2F71f10900-8562-42d5-a802-abdacc092017%2F39j7qyn_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose you have the following pre-test and post-test scores for a random sample of five students.
| Student | 1 | 2 | 3 | 4 | 5 |
|---------|----|----|----|----|----|
| Pre-test | 63 | 73 | 54 | 56 | 52 |
| Post-test| 94 | 95 | 86 | 84 | 97 |
We would like to test the hypotheses \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d > 0 \), where \( \mu_d \) is the mean difference in pre-test and post-test scores for all students (post - pre).
*(a) We would like to carry out a t test for the population mean difference. Calculate the point estimate.*
[Text box]
*(b) If the null hypothesis is true, the t test statistic follows a t distribution. How many degrees of freedom does it have?*
[Text box]
*(c) Suppose the p-value of this test turned out to be less than 0.001. Which of the following is the correct conclusion? Use \(\alpha = 0.05\).*
- ○ We have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is less than zero.
- ○ We have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is greater than zero.
- ○ We do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is less than zero.
- ○ We do not have enough evidence to conclude that the population mean difference in pre-test and post-test scores (post - pre) is greater than zero.
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