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, 11 answered the questionaccurately. The second random sample consisted of 43 people who hadbeen charged with drunken driving. During a telephone interview, 28of 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. Please show all steps in getting the answer.

(a) Categorize the problem below according to parameter beingestimated, proportion p, mean ?, difference of means ?1 – ?2, ordifference of proportions p1 – p2. Then solve the problem.

?

?1 – ?2

p

p1 – p2

(b) Let p1 represent the population proportion of all peoplewith recent charges of drunken driving who respond accurately to aface-to-face interview asking if they have been charged withdrunken driving during the past 12 months. Let p2 represent thepopulation proportion of all people who respond accurately to thequestion when it is asked in a telephone interview. Find a 95%confidence interval for p1 – p2. (Use 3 decimal places.)

lower limit

upper limit

(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 95%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 positive and negativenumbers, we can not say that there is a higher proportion ofaccurate responses in face-to-face interviews.

We can not make any conclusions using this confidenceinterval.

Because the interval contains only negative numbers, we can saythat there is a higher proportion of accurate responses intelephone interviews.