Answer Happy

Investigation 2: Do Incentives Work? A team of researchersinvestigated whether incentives would improve the response rates ona telephone survey. A random sample of 735 households from thestate of Virginia was selected and all 735 of the households weresent an “advance letter” explaining that the household would becontacted shortly for a telephone survey. However, 368 householdswere randomly assigned to receive a monetary incentive along withthe advance letter, and the other 367 households were assigned toreceive only the advance letter. The results showed that 286households that received the monetary incentive responded to thesurvey whereas 245 households that did not receive the incentiveresponded to the survey. a) What is the parameter of interest? Usewords and a symbol(s) in context in your answer. Define any symbolsthat you use. b) Calculate and label the two sample proportionsseparately. Next, calculate the difference between these sampleproportions by subtracting (Incentive – No incentive). Completethese calculations by hand, label each of them, and present each ofthese values in your solutions document rounded to four decimalplaces. c) Create a bootstrap distribution. In StatKey under themiddle pane labeled ‘Bootstrap Confidence Intervals’, click CI forDifference in Proportions. Click ‘Edit Data’, then enter in thecount and sample size for each group. Make Group 1 those thatreceived a monetary incentive and Group 2 those that only receiveda letter. Next, click ‘Generate 1000 Samples.’ Copy (i.e. take ascreenshot) your graph into your solutions document. d) Describethe shape of the bootstrap distribution. e) Construct a 95%bootstrap confidence interval using the + 2SE method. Show all workand present your answer in this format (lower value, upper value).f) Interpret the meaning of the confidence interval in context. g)Does your confidence interval capture 0? Based on your answer, canwe infer anything about whether incentives work stated in theproblem? Answer these questions in one or two sentences. h) Can wegeneralize to a larger group or speak about a cause-and-effectrelationship (or both)? Answer this question in one or twosentences and please provide a reason in your answer. i) What wouldhappen to the confidence interval if we changed the sample size?Let’s say we had the ability to sample 1200 people, 600 in eachgroup. Go to Edit Data and enter in the counts and sample sizes foreach group (the counts are 466 for Group 1 and 400 for Group 2).Construct another 95% bootstrap confidence interval and comparethis interval to the one found in part 2(e).