Survey Response: Validity A study was conducted to determine accuracy of answers to questions from surveys. In the study, the question “Are you a registered voter?” was considered. Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a face-to-face interview and by email. A random sample of 93 people was 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 was asked the same question by email. 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 by email. Find a 95% confidence interval for p1 2p2.

(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-toface interviews compared with the proportion of accurate responses from emails?

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