From public records, individuals were identified as having beencharged with drunken driving not less than 6 months or more than 12months from the starting date of the study. Two random samples fromthis group were studied. In the first sample of 29 individuals, therespondents were asked in a face-to-face interview if they had beencharged with drunken driving in the last 12 months. Of these 29people interviewed face to face, 12 answered the questionaccurately. The second random sample consisted of 41people who hadbeen charged with drunken driving. During a telephone interview, 23of these responded accurately to the question asking if they hadbeen charged with drunken driving during the past 12 months. Assumethe samples are representative of all people recently charged withdrunken driving.
(a) Categorize the problem below according to parameter beingestimated, proportion p, mean μ, difference ofmeans μ1 – μ2, ordifference of proportions p1 –p2. Then solve the problem.
μ1 –μ2p     p1– p2μ
(b) Let p1 represent the population proportionof all people with recent charges of drunken driving who respondaccurately to a face-to-face interview asking if they have beencharged with drunken driving during the past 12 months. Letp2 represent the population proportion of allpeople who respond accurately to the question when it is asked in atelephone interview. Find a 99% confidence interval forp1 – p2. (Use 3 decimalplaces.)
(c) Does the interval found in part (a) contain numbers that areall positive? all negative? mixed? Comment on the meaning of theconfidence interval in the context of this problem. At the 99%level, do you detect any differences in the proportion of accurateresponses to the question from face-to- face interviews as comparedwith the proportion of accurate responses from telephoneinterviews?
Because the interval contains only positive numbers, we can saythat there is a higher proportion of accurate responses inface-to-face interviews.Because the interval contains both positiveand negative numbers, we can not say that there is a higherproportion of accurate responses in face-to-faceinterviews.     We can not make anyconclusions using this confidence interval.Because the intervalcontains only negative numbers, we can say that there is a higherproportion of accurate responses in telephone interviews.
