Investigation 3: Do Incentives Work? (no data set) A team of researchers investigated whether incentives would improve the response rates on a telephone survey. A random sample of 735 households from the state of Virginia was selected and all 735 of the households were sent an "advance letter" explaining that the household would be contacted shortly for a telephone survey. However, 368 households were randomly assigned to receive a monetary incentive along with the advance letter, and the other 367 households were assigned to receive only the advance letter. The results showed that 286 households that received the monetary incentive responded to the survey whereas 245 households that did not receive the incentive responded to the survey.

a) Calculate and label the two sample proportions separately. Next, calculate the difference between these sample proportions by subtracting (Incentive - No incentive). Complete these calculations by hand, label each of them, and present each of these values in your solutions document rounded to four decimal places.

b) Check the Central Limit Theorem conditions for a confidence interval for the difference between two proportions. For the large sample condition, check and show that each sample has at least 10 successes and 10 failures.

c) Construct the 95% confidence interval

d) Interpret the 95% confidence interval in context in one sentence. In your interpretation, round the confidence limits to four decimal places.

e) Does your confidence interval capture 0? Based on your answer, can we infer anything about whether incentives work stated in the problem? Answer these question in one or two sentences.

f) Can we generalize to a larger group or speak about a cause-and-effect relationship (or both)? Answer this questions in one or two sentences and please provide a reason in your answer