### Do Political Science Classes Require More Writing Than History Classes?**Question Context:**The study examines whether political science classes require more writing compared to history classes. Statistical data has been gathered as follows:- **Political Science Classes:** - Sample Size (n1): 56 classes - Average Pages of Writing: 18.1 pages - Standard Deviation: 5.8 pages- **History Classes:** - Sample Size (n2): 54 classes - Average Pages of Writing: 15.5 pages - Standard Deviation: 3.9 pagesSignificance level (α) is set at 0.05.**a. Formulating Hypotheses:**The null and alternative hypotheses need to be established.- **Null Hypothesis (H0)**: - \( \mu_1 - \mu_2 = 0 \) - (The mean number of pages of writing required for political science classes is equal to that of history classes).- **Alternative Hypothesis (H1)**: - \( \mu_1 - \mu_2 > 0 \) - (The mean number of pages of writing required for political science classes is greater than that of history classes).**b. The Test Statistic:**The appropriate test statistic for this hypothesis test will be calculated using the sample means, standard deviations, and sample sizes. Please provide your answer to 3 decimal places.**c. P-value Calculation:**The p-value corresponding to the test statistic should be calculated. Please provide your answer to 4 decimal places.**d. Decision Criterion:**Determine if the p-value is less than or equal to the significance level \( \alpha \).- **Is the p-value ≤ \( \alpha \)?****e. Conclusion Based on Null Hypothesis:**Based on the p-value, decide whether to reject or fail to reject the null hypothesis.**f. Final Conclusion:**Depending on whether the null hypothesis is rejected or not, the final conclusion will be one of the following statements:1. If the results are statistically significant at \( \alpha = 0.05 \): - There is sufficient evidence to conclude that the population mean number of pages of writing that political science classes require is more than the population mean number of pages of writing that history classes require.2. If the results are statistically insignificant at \( \alpha =

Given n1=56 n2=54 X1-bar=18.1 X2-bar=15.5

Do political science classes require more writing than history classes? The 56 randomly selected political science classes assigned an average of 18.1 pages of essay writing for the course. The standard deviation for these 56 classes was 5.8 pages. The 54 randomly selected history classes assigned an average of 15.5 pages of essay writing for the course. The standard deviation for these 54 classes was 3.9 pages. What can be concluded at the a = 0.05 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer Select an answer Select an answer H₁: Select an answer Select an answer Select an answer b. The test statistic ? :- (please show your answer to 3 decimal places.) c. The p-value= (Please show your answer to 4 decimal places.) d. The p-value is? : e. Based on this, we should f. Thus, the final conclusion is that ... Select an answer the null hypothesis. The results are statistically significant at a = 0.05, so there is sufficient evidence to conclude that the population mean number of pages of writing that political science classes require is more than the population mean number of pages of writing that history classes require. The results are statistically insignificant at a = 0.05, 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. The results are statistically significant at a = 0.05, so there is sufficient evidence to conclude that the mean number of required pages for the 56 political science classes that were observed is more than the mean number of required pages for the 54 history classes that were observed. The results are statistically insignificant at a = 0.05, so there is insufficient evidence to conclude that the population mean number of pages of writing that political science classes require is more than the population mean number of pages of writing that history classes require.