Suppose you run two different email ad campaigns over many days and record the amount of traffic driven to your website on days that each ad is sent. in particular, suppose that ad 2 is sent on 50 different days and generates an average of 2 million page views per day with a standard deviation of 1 million views, and ad 1 is sent on 40 different days and generates an average of 2.5 million page views per day with a standard deviation of a half million views.
(a) to learn about the difference (if one exists) between ad 2's average page views per day and ad 1's average page views per day, compute a 95% confidence interval for the difference between the ads' average page views. interpret your confidence interval.
(b) your boss, dr. ana maria ferguson, tells you that you can run 10 more days of experiments in order to refine your confidence interval from part (a). which of the following strategies would most reduce the width of the confidence interval, assuming that your estimates of the means and standard deviations would not change? explain your choice.
i. spend 8 days testing ad 2 and 2 days testing ad 1
ii. spend all 10 days testing ad 2 .
iii. spend all 10 days testing ad 1
iv. spend 5 days testing each
(c) based on the original data (no additional days testing), dr. ferguson wants to know if there is enough evidence that ad 1 outperforms ad 2 by at least 150,000 views per day at the a = 0.01 level. state the relevant null and alternative hypotheses. perform a hypothesis test to answer dr. ferguson's question.