Q2 [14 pts] Compare two teaching methods. A researcher wants to compare the average test scores of two different teaching methods, but it is unclear which method is better. Method A is a traditional lecture-based approach, while method B involves more interactive group-based activities. The researcher randomly assigns 30 students to each method and administers the same test at the end of the semester. The results are summarized in the following table: Method Sample standard deviation A B Sample size 30 30 Sample mean 75 80 10 12 Furthermore, we assume the test score in both methods are normally distributed. (a) [1 pt] What is the design used in this experiment? (b) [2 pts] State the null and alternative hypotheses for this two-sample t-test. (c) [2 pts] What is the observed test statistic value? Round result up to second decimal places. (d) [2 pts] Determine the degrees of freedom using option 1 for this test, round the result to the nearest whole number. (e) [2 pts] Determine the range for the p-value (df from option 1) using Table C (attached at the end). (f) [2 pts] Set the significance level at 5%. Make a decision to reject or fail to reject the null hypothesis based on p-value obtained in part (d). Further interpret the results in the context of the study. (g) [3 pts] To find the 95% confidence interval the mean difference between method B and A (B - HA), what is the critical value (df with option 2) using Table C? What is the lower bound and upper bound in the 95% CI. Rounding your result up to 4 decimal places.