\\ l \\ A I L A 6. Aboredstatisticianbelievestheaveragelength(pg)ofcommercialbreakson cable channels (ESPN, TNT, etc.) is longer than the average length (MN) of commercial breaks on the networks. He times a random sample of commercials from each of the two types of broadcasts. (Assume the lengths of commercial breaks from both types of broadcasts follow normal distributions) Source Sample Size Mean Standard Deviation Cable 15 2.36 0.16 Network 12 2.18 0.13 (a) (3 points) Can we assume equal variances here? Please provide an Ftest. Page 3 of 4 STAT 703 TakeHome Final Exam Fall 2021 (b) (2 points) What are the appropriate hypotheses to determine if there is signicant evidence to support the statistician's claim? (c) (2 points) Assuming equal variances, what is your estimate of the common variance? (pooled sample variance) (d) (3 points) Construct the test statistic for hypotheses test in (b) by using the common variance. How many degrees of freedom it has? (e) (2 points) What is the rejection region for testing the hypotheses in (b)? Please give your conclusions. (f) (2 points) Please provide the pvalue. (g) (3 points) Please construct a two-sided 95% condence interval for no MN