Question

3. Two classes of statistics were taught by one instructor. Class A was evaluated using weekly team-based learning exercises, quizzes and a final exam. Class B had a midterm and final exam Both classes were provided the same set of practice assignments. From a particular term, it was found that in Class A, 48 of 120 students attained an A- or better upon completion of the course. In Class B, 30 of 100 students attained A- or better. a) Is there evidence that the proportions of students attaining A- or better in Class A and in Class B are different? Use a significance level of 0.05. b) Construct a 95% confidence interval for the difference between the proportions of students attaining A-or better in Class A and in Class B. Can you make the same conclusion as in part a?d el

Answer 1

A - 1

B - 2

For sample 1, we have that the sample size is M 120, the number of favorable cases is Xi - 48, so then the sample proportion is pi0.4 For sample 2, we have that the sample size is 2 100, the number of favorable casos is X 30, so then the sample proportion is p00.3 The value of the pooled proportion is computed as p-NEN| 0.3545 Also, the given significance level is-0.05 The following null and alternative hypotheses need to be tested Ho: Pi-P2 This corresponds to a two tailed test, for which a z tost for two population proportions needs to be conducted. Based on the information provided, the significance level is a0.05, and the critical value for a two tailed testis1.96 The rejection region for this two-teiled tests R = {z : Izl > 1.96} (3) Test Statistics The z-statistic is computed as follows. 0.4 0.3 1.514 Vp( p)(1/ni +1/n2) 0.35451 0.3545) (1/120+1/100) 4) Decision about the nul hypothesis Since it is observed that1.514 1.96, it is then concluded that the nul hypothesis is not rejected Using the P-value approach: The p-value is 0.1226, and since p-0.1226 > 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 proportion pi is different than p2, at the 0.05 significance level. val The 95% confidence interval for P1-P2 is:-0.025 P1-P2 < 0.225 Grephicelly Z-test for Two Proportions. z-1.544. p-0.1226 0.30 0.20 0.15 0.10 0.05 0 Co 40.35 .30-25-20.15-1.0.0 5 ถถ ถ5 10 15 2.ถ 25ョ0 35 4a

B)

CONFIDENCE INTERVAL =(-0.025,0.225)

since 0 is present in confidence interval

we fail to reject the null

hence same conclusion as in part (a)