Homework: Matched or Paired SamplesYou wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test. Ho:μd=0Ho:μd=0 Ha:μd>0Ha:μd>0You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:\pre-testpost-test42.584.742.556.241.566.231.954.240.488.133.443.137.870.736.262.545.793.437.516.852.18536.257.73865.146.513841.568.649.353.144.321.842.95143.17640.968.84462.447.553.9What is the test statistic for this sample?test statistic = Incorrect4.6975 (Report answer accurate to 4 decimal places.)What is the p-value for this sample?p-value = Incorrect0.0001 (Report answer accurate to 4 decimal places.)The p-value is...less than (or equal to) ααgreater than ααCorrectThis test statistic leads to a decision to...reject the nullaccept the nullfail to reject the nullCorrectAs such, the conclusion is that...There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.PLEASE INCLUDE CALCULATOR STEPS ON TI 84 You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.002\). For the context of this problem, \(\mu_d = \mu_2 - \mu_1\) where the first data set represents a pre-test and the second data set represents a post-test.- \(H_0: \mu_d = 0\)- \(H_a: \mu_d > 0\)You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:| pre-test | post-test ||----------|-----------|| 42.5 | 84.7 || 42.5 | 56.2 || 41.5 | 66.2 || 31.9 | 54.2 || 40.4 | 88.1 || 33.4 | 43.1 || 37.8 | 70.7 || 36.2 | 62.5 || 45.7 | 93.4 || 37.5 | 16.8 || 52.1 | 85 || 36.2 | 57.7 || 38 | 65.1 || 46.5 | 138 || 41.5 | 68.6 || 49.3 | 53.1 || 44.3 | 21.8 || 42.9 | 51 || 43.1 | 76 || 40.9 | 68.8 || 44 | 62.4 || 47.5 | 53.9 |### Test Statistics and P-value- **Test Statistic**: 4.6975 (report accurate to 4 decimal places).- **P-value**: 0.0001 (report accurate to 4 decimal places).### P-value Analysis- The p-value is less than (or equal to) \(\alpha\).### Conclusion Based on Test Statistics- **Decision**: Reject the null hypothesis.### Final Conclusion

It has been believed that the population of difference scores is normally distributed.

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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Homework: Matched or Paired Samples

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test.

Ho:μd=0Ho:μd=0
Ha:μd>0Ha:μd>0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:\

pre-test	post-test
42.5	84.7
42.5	56.2
41.5	66.2
31.9	54.2
40.4	88.1
33.4	43.1
37.8	70.7
36.2	62.5
45.7	93.4
37.5	16.8
52.1	85
36.2	57.7
38	65.1
46.5	138
41.5	68.6
49.3	53.1
44.3	21.8
42.9	51
43.1	76
40.9	68.8
44	62.4
47.5	53.9

What is the test statistic for this sample?
test statistic = Incorrect4.6975 (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?
p-value = Incorrect0.0001 (Report answer accurate to 4 decimal places.)

The p-value is...

less than (or equal to) αα
greater than αα

Correct

This test statistic leads to a decision to...

reject the null
accept the null
fail to reject the null

Correct

As such, the conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.
There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.

PLEASE INCLUDE CALCULATOR STEPS ON TI 84

You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.002\). For the context of this problem, \(\mu_d = \mu_2 - \mu_1\) where the first data set represents a pre-test and the second data set represents a post-test.

- \(H_0: \mu_d = 0\)
- \(H_a: \mu_d > 0\)

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

| pre-test | post-test |
|----------|-----------|
| 42.5 | 84.7 |
| 42.5 | 56.2 |
| 41.5 | 66.2 |
| 31.9 | 54.2 |
| 40.4 | 88.1 |
| 33.4 | 43.1 |
| 37.8 | 70.7 |
| 36.2 | 62.5 |
| 45.7 | 93.4 |
| 37.5 | 16.8 |
| 52.1 | 85 |
| 36.2 | 57.7 |
| 38 | 65.1 |
| 46.5 | 138 |
| 41.5 | 68.6 |
| 49.3 | 53.1 |
| 44.3 | 21.8 |
| 42.9 | 51 |
| 43.1 | 76 |
| 40.9 | 68.8 |
| 44 | 62.4 |
| 47.5 | 53.9 |

### Test Statistics and P-value

- **Test Statistic**: 4.6975 (report accurate to 4 decimal places).
- **P-value**: 0.0001 (report accurate to 4 decimal places).

### P-value Analysis
- The p-value is less than (or equal to) \(\alpha\).

### Conclusion Based on Test Statistics
- **Decision**: Reject the null hypothesis.

### Final Conclusion

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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