a. The null and alternative hypotheses would be: Ho: Select an answer H₁: Select an answer Select an answer Select an answer Select an answer ✓ Select an answer (please show your answer to 3 decimal places.) b. The test statistic c. The p-value= d. The p-value is [?✔a e. Based on this, we should Select an answer the null hypothesis. f. Thus, the final conclusion is that ... (Please show your answer to 4 decimal places.) O The results are statistically insignificant at a = 0.10, so there is insufficient evidence to conclude that the population mean number of pages of writing that political science classes require is less than the population mean number of pages of writing that history classes require. O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the population mean number of pages of writing that political science classes require is less than the population mean number of pages of writing that history classes require. O The results are statistically insignificant at a = 0.10, so there is statistically significant evidence to conclude that the population mean number of pages of writing that political science classes require is equal to the population mean number of pages of writing that history classes require. O The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the mean number of required pages for the 44 political science classes that were observed is less than the mean number of required pages for the 42 history classes that were observed.

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**Educational Content: Hypothesis Testing on Writing Requirements in Political Science vs. History Classes**

**Research Question:**
Do political science classes require less writing than history classes? 

**Study Details:**
- **Political Science Classes**: 44 classes, average writing = 14.9 pages, standard deviation = 4.9 pages.
- **History Classes**: 42 classes, average writing = 17.8 pages, standard deviation = 5.6 pages.

**Statistical Analysis:**

For this study, you should select an appropriate test (e.g., t-test) to compare the means.

**a. Hypotheses:**

- **Null Hypothesis (\(H_0\))**: Mean pages of writing for political science = Mean pages of writing for history.
- **Alternative Hypothesis (\(H_1\))**: Mean pages of writing for political science < Mean pages of writing for history.

**b. Test Statistic:**
Calculate the test statistic (\( t \)) and round your answer to three decimal places.

**c. P-value:**
Determine the p-value and round your answer to four decimal places.

**d. Significance:**
Compare the p-value to the significance level (\( \alpha = 0.10 \)).

**e. Decision:**
Select whether to reject or fail to reject the null hypothesis based on the p-value.

**f. Conclusion:**
Choose the correct conclusion:
1. Results are statistically insignificant at \( \alpha = 0.10 \), insufficient evidence that political science classes require less writing.
2. Results are statistically significant, sufficient evidence that political science classes require less writing.
3. Results are insignificant, population mean number of pages for political science equals history.
4. Results are significant, the required pages for political science classes observed are less than for history classes observed. 

This setup guides the process of hypothesis testing to determine differences in writing requirements between political science and history classes.
Transcribed Image Text:**Educational Content: Hypothesis Testing on Writing Requirements in Political Science vs. History Classes** **Research Question:** Do political science classes require less writing than history classes? **Study Details:** - **Political Science Classes**: 44 classes, average writing = 14.9 pages, standard deviation = 4.9 pages. - **History Classes**: 42 classes, average writing = 17.8 pages, standard deviation = 5.6 pages. **Statistical Analysis:** For this study, you should select an appropriate test (e.g., t-test) to compare the means. **a. Hypotheses:** - **Null Hypothesis (\(H_0\))**: Mean pages of writing for political science = Mean pages of writing for history. - **Alternative Hypothesis (\(H_1\))**: Mean pages of writing for political science < Mean pages of writing for history. **b. Test Statistic:** Calculate the test statistic (\( t \)) and round your answer to three decimal places. **c. P-value:** Determine the p-value and round your answer to four decimal places. **d. Significance:** Compare the p-value to the significance level (\( \alpha = 0.10 \)). **e. Decision:** Select whether to reject or fail to reject the null hypothesis based on the p-value. **f. Conclusion:** Choose the correct conclusion: 1. Results are statistically insignificant at \( \alpha = 0.10 \), insufficient evidence that political science classes require less writing. 2. Results are statistically significant, sufficient evidence that political science classes require less writing. 3. Results are insignificant, population mean number of pages for political science equals history. 4. Results are significant, the required pages for political science classes observed are less than for history classes observed. This setup guides the process of hypothesis testing to determine differences in writing requirements between political science and history classes.
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