You wish to test the following claim (H) at a significance level of a = 0.10. For the context of this problem, µd is the true mean difference in scores on pre-test and post-test (post-test - pre-test). Н.: ра — 0 0 > Prd :"H You believe the population of difference in scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n = 23 subjects. The average difference (post - pre) is d = – 17.7 with a standard deviation of the differences of sd = 44.6. What is the test statistic for this sample? (Report answer accurate to 4 decimal places.) test statistic = What is the p-value for this test? (Report answer accurate to 4 decimal places.) p-value = The test statistic is... O in the rejection region O not in the rejection region This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0. O There is not sufficient evidence to warrant rejection of the claim that the mean difference of post- test from pre-test is less than 0. O The sample data support the claim that the mean difference of post-test from pre-test is less than 0. O There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.
You wish to test the following claim (H) at a significance level of a = 0.10. For the context of this problem, µd is the true mean difference in scores on pre-test and post-test (post-test - pre-test). Н.: ра — 0 0 > Prd :"H You believe the population of difference in scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n = 23 subjects. The average difference (post - pre) is d = – 17.7 with a standard deviation of the differences of sd = 44.6. What is the test statistic for this sample? (Report answer accurate to 4 decimal places.) test statistic = What is the p-value for this test? (Report answer accurate to 4 decimal places.) p-value = The test statistic is... O in the rejection region O not in the rejection region This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null As such, the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0. O There is not sufficient evidence to warrant rejection of the claim that the mean difference of post- test from pre-test is less than 0. O The sample data support the claim that the mean difference of post-test from pre-test is less than 0. O There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![## Hypothesis Testing of Pre-test and Post-test Scores at Significance Level α = 0.10
In this scenario, we are testing the following claims regarding the mean difference in scores from pre-test to post-test:
Null Hypothesis (\(H_0\)):
\[ \mu_d = 0 \]
Alternative Hypothesis (\(H_a\)):
\[ \mu_d < 0 \]
Where \(\mu_d\) represents the true mean difference in scores on pre-test and post-test (post-test - pre-test).
### Given Data:
- The population of difference in scores is assumed to be normally distributed.
- Sample size (\(n\)) = 23 subjects
- Average difference (post - pre) (\(\bar{x}_d\)) = -17.7
- Standard deviation of the differences (\(s_d\)) = 44.6
### Statistical Analysis:
1. **Test Statistic Calculation**:
\[ \text{Test statistic} = \boxed{\quad} \]
2. **P-value Calculation**:
\[ \text{P-value} = \boxed{\quad} \]
### Evaluation of the Test Statistic:
- The test statistic is:
\[ \text{o in the rejection region} \]
\[ \text{o not in the rejection region} \]
### Decision Making:
Based on the test statistic, we reach one of the following decisions:
- \(\text{o reject the null}\)
- \(\text{o accept the null}\)
- \(\text{o fail to reject the null}\)
### Conclusion:
As a result, the final conclusion could be:
- \(\text{o There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.}\)
- \(\text{o There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.}\)
- \(\text{o The sample data support the claim that the mean difference of post-test from pre-test is less than 0.}\)
- \(\text{o There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48699ae0-6c1f-4889-b5a2-9929e5766b17%2Fa5225110-8614-40c3-b0a5-6fac7c514d48%2F9pd3ptu_processed.png&w=3840&q=75)
Transcribed Image Text:## Hypothesis Testing of Pre-test and Post-test Scores at Significance Level α = 0.10
In this scenario, we are testing the following claims regarding the mean difference in scores from pre-test to post-test:
Null Hypothesis (\(H_0\)):
\[ \mu_d = 0 \]
Alternative Hypothesis (\(H_a\)):
\[ \mu_d < 0 \]
Where \(\mu_d\) represents the true mean difference in scores on pre-test and post-test (post-test - pre-test).
### Given Data:
- The population of difference in scores is assumed to be normally distributed.
- Sample size (\(n\)) = 23 subjects
- Average difference (post - pre) (\(\bar{x}_d\)) = -17.7
- Standard deviation of the differences (\(s_d\)) = 44.6
### Statistical Analysis:
1. **Test Statistic Calculation**:
\[ \text{Test statistic} = \boxed{\quad} \]
2. **P-value Calculation**:
\[ \text{P-value} = \boxed{\quad} \]
### Evaluation of the Test Statistic:
- The test statistic is:
\[ \text{o in the rejection region} \]
\[ \text{o not in the rejection region} \]
### Decision Making:
Based on the test statistic, we reach one of the following decisions:
- \(\text{o reject the null}\)
- \(\text{o accept the null}\)
- \(\text{o fail to reject the null}\)
### Conclusion:
As a result, the final conclusion could be:
- \(\text{o There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.}\)
- \(\text{o There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.}\)
- \(\text{o The sample data support the claim that the mean difference of post-test from pre-test is less than 0.}\)
- \(\text{o There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.}\)
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