Please answer B, C, & D. **Examining the Impact of Colored Pens on Final Exam Scores****Context:**A professor aimed to determine if the use of colored pens affected students' average final exam scores in a statistics course, where the standard average score is 82%. Thirteen students who received colored pens on the first day of class had the following scores:99, 89, 68, 88, 75, 89, 85, 93, 83, 68, 84, 91, 81.The objective was to assess any statistically significant changes at the $\alpha = 0.05$ significance level.**Statistical Analysis:**a. **Test Selection:** - **Chosen Test:** t-test for a population mean.b. **Hypotheses:** - **Null Hypothesis ($H_0$):** The population mean is equal to 82. - **Alternative Hypothesis ($H_1$):** The population mean is not equal to 82.c. **Calculation of the Test Statistic:** - Test statistic ($t$) value: Calculated to three decimal places.d. **Determination of the P-value:** - P-value: Calculated to four decimal places.e. **Comparison with Significance Level ($\alpha$):** - Decision rule applied: $p > \alpha$.f. **Conclusion Regarding Hypothesis:** - Null hypothesis decision: Fail to reject the null hypothesis.g. **Final Conclusion:** - **Selected Conclusion:** The data suggest that the population mean final exam score for students who are given colored pens is not significantly different from 82 at $\alpha = 0.05$. Hence, there is statistically insignificant evidence to conclude any difference in mean scores for these students.**Visual Component:**The image provides options for each part of the analysis, including hypothesis choices and results. The final conclusion is highlighted and confirmed as statistically insignificant in showing differences from the average score.This analysis illustrates the application of hypothesis testing in educational settings to evaluate potential impacts of teaching tools on student performance.

Answered: Image /qna-images/answer/a0f92c43-32a8-4d56-8a83-ba5be15b550e.jpg

b. The null and alternative hypotheses would be: Ho: ?v Select an answer H1: ?v Select an answer ♥ c. The test statistic ?v (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) %3D

b. The null and alternative hypotheses would be: Ho: ?v Select an answer H1: ?v Select an answer ♥ c. The test statistic ?v (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) %3D

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Please answer B, C, & D.

**Examining the Impact of Colored Pens on Final Exam Scores**

**Context:**
A professor aimed to determine if the use of colored pens affected students' average final exam scores in a statistics course, where the standard average score is 82%. Thirteen students who received colored pens on the first day of class had the following scores:
99, 89, 68, 88, 75, 89, 85, 93, 83, 68, 84, 91, 81.

The objective was to assess any statistically significant changes at the $\alpha = 0.05$ significance level.

**Statistical Analysis:**

a. **Test Selection:**
- **Chosen Test:** t-test for a population mean.

b. **Hypotheses:**
- **Null Hypothesis ($H_0$):** The population mean is equal to 82.
- **Alternative Hypothesis ($H_1$):** The population mean is not equal to 82.

c. **Calculation of the Test Statistic:**
- Test statistic ($t$) value: Calculated to three decimal places.

d. **Determination of the P-value:**
- P-value: Calculated to four decimal places.

e. **Comparison with Significance Level ($\alpha$):**
- Decision rule applied: $p > \alpha$.

f. **Conclusion Regarding Hypothesis:**
- Null hypothesis decision: Fail to reject the null hypothesis.

g. **Final Conclusion:**
- **Selected Conclusion:** The data suggest that the population mean final exam score for students who are given colored pens is not significantly different from 82 at $\alpha = 0.05$. Hence, there is statistically insignificant evidence to conclude any difference in mean scores for these students.

**Visual Component:**
The image provides options for each part of the analysis, including hypothesis choices and results. The final conclusion is highlighted and confirmed as statistically insignificant in showing differences from the average score.

This analysis illustrates the application of hypothesis testing in educational settings to evaluate potential impacts of teaching tools on student performance.

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