a) Suppose you are a researcher investigating the effeciveness of two diflerent teaching nethots A mid on Sample A (Method A): Sample size (n1):150 Number of students who passed: 105 Sample B (Method B) : Sample size (n2):180 Number of students who passed: 135 Assume a significance level ( a ) of 0.05 . Examine to determine if there is a signifart difference in the propotions of students passing between the two teaching methods Use critucal value of 2 statistic as 155. [3] b) A random sample of 50 students was taken to estimate the average time (in minute) they spend on horeach each day. The sample mean is 120 minutes, and the sample standard devation is 15 minutes. Calculate a 95% confidence interval for the true average time spent on homework per day. [II Justify your answer [2]