3. You are testing two versions of a software interface: Version 2.7a and Version 2.7b. Management believes that people are equally satisfied with the two versions. You want to challenge this idea, but you're not sure whether users prefer 2.7a or 2.7b. On average, you expect about 50% of the users will express high satisfaction with either interface. Management indicates that if the high satisfaction rates are within 10%, they consider them equally acceptable - they only want to know if the high satisfaction rates differ by more than 10%. a. How many observations should you have from each population (users of Version 2.7a and users of Version 2.7b) in order to be able to detect a difference of at least 10%, with 80% power, in the proportion of respondents that indicate "high satisfaction" with the interface? b. If you expect a 30% response rate to your survey, how many people should you survey for each interface? c. Suppose you send out the number of surveys you calculated in 3a, and get a response rate of 35% for both surveys. Of the surveys returned, 55% indicated high satisfaction with Version 2.7a, and 46% indicated high satisfaction with Version 2.7b. Given this data, conduct a two-sample test of proportions where HO: p1 - p2 = 0 vs H1: p1 - p2 = 0 and pi refers to the proportion of people who expressed high satisfaction for Version 2.7a, and pz refers to the proportion of people who expressed high satisfaction for Version 2.7b. Draw a conclusion using a = 0.10. (Hint: you can do this by using Stat > Basic Statistics > 2 Proportions and selecting "Summarized data" in the dropdown box.) d. Your boss asks you which version to use. What evidence do you have for using one version or the other