Question

Do political science classes require the same amount of writing as history classes? The 41 randomly selected political science classes assigned an average of 15.8 pages of essay writing for the course. The standard deviation for these 41 classes was 3.4 pages. The 46 randomly selected history classes assigned an average of 16.5 pages of essay writing for the course. The standard deviation for these 46 classes was 4.8 pages. What can be concluded at the αα = 0.05 level of significance?

For this study, we should use Select an answer z-test for the difference between two population proportions t-test for a population mean t-test for the difference between two dependent population means t-test for the difference between two independent population means z-test for a population proportion

1. The null and alternative hypotheses would be:   
2.   

H0:H0:  Select an answer p1 μ1  ? = ≠ < >  Select an answer μ2 p2  (please enter a decimal)   

H1:H1:  Select an answer p1 μ1  ? = ≠ < >  Select an answer p2 μ2  (Please enter a decimal)

2. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? ≤ >  αα
5. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.

Answer 1

t-test for the difference between two independent population

ses The following null and alternative hypotheses need to be tested This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used (2) Rejection Region Based on the information provided, the significance level is α = 0.05, and the degrees of freedom are df 85. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal Hence, it is found that the critical value for this two-tailed test is tc 85 1.988, for a 0.05 and df - The rejection region for this two-tailed test is R ft: t1.988 Since it is assumed that the population variances are equal, the t-statistic is computed as follows 1 15.8 16.5 41-13.42+(46-1)4.8 -0.776 (4) Decision about the null hypothesis Since it is observed tha0.776e1.988, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p 0.4399, and since p 0.4399> 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μι is different than μ , at the 0.05 significance level The 95% confidence interval is 2.493 < 1 t2 < 1.093