Survey Response: Validity The book Survey Responses: An Evaluation of Their Validity by E. J. Wentland and K. Smith (Academic Press), includes studies reporting accuracy of answers to questions from surveys. A study by Locander et al. considered the question “Are you a registered voter?” Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a face-to-face interview and a telephone interview. A random sample of 93\ people were asked the voter registration question face-to-face. Seventy-nine respondents gave accurate answers (as verified by city records). Another random sample of 83 people were asked the same question during a telephone interview. Seventy-four respondents gave accurate answers. Assume the samples are representative of the general population.

(a) Let p₁ be the population proportion of all people who answer the voter registration question accurately during a face-to-face interview. Let p₂ be the population proportion of all people who answer the question accurately during a telephone interview. Find a 95% confidence interval for p₁- p₂.

(b) Interpretation Does the interval contain numbers that are all positive? All negative? mixed? Comment on the meaning of the confidence interval in the context of this problem. At the 95% level, do you detect any difference in the proportion of accurate responses from face-to-face interviews compared with the proportion of accurate responses from telephone interviews?