From public records, individuals were identified as having been charged with dru

Question

From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the study. Two random samples from this group were studied. In the first sample of 31 individuals, the respondents were asked in a face-to-face interview if they had been charged with drunken driving in the last 12 months. Of these 31 people interviewed face to face, 12 answered the question accurately. The second random sample consisted of 46people who had been charged with drunken driving. During a telephone interview, 21 of these responded accurately to the question asking if they had been charged with drunken driving during the past 12 months. Assume the samples are representative of all people recently charged with drunken driving.

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

1.) 1 – 2

2.) p     

3.)

4.) p1 – p2

(b) Let p1 represent the population proportion of all people with recent charges of drunken driving who respond accurately to a face-to-face interview asking if they have been charged with drunken driving during the past 12 months. Let p2 represent the population proportion of all people who respond accurately to the question when it is asked in a telephone interview. Find a 99% confidence interval for p1 – p2. (Use 3 decimal places.)

(c) Does the interval found in part (a) 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 99% level, do you detect any differences in the proportion of accurate responses to the question from face-to- face interviews as compared with the proportion of accurate responses from telephone interviews?

1.) Because the interval contains only positive numbers, we can say that there is a higher proportion of accurate responses in face-to-face interviews.

2.) Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of accurate responses in face-to-face interviews.   

3.) We can not make any conclusions using this confidence interval.

4.) Because the interval contains only negative numbers, we can say that there is a higher proportion of accurate responses in telephone interviews.

Explanation / Answer

a) Option - 4) p1 - p2

b) p1 = 12/31 = 0.387

p2 = 21/46 = 0.457

Pooled sample proportion (P) = (p1 * n1 +p2 * n2)/(n1 + n2)

                                                 = (0.387 * 31 + 0.457 * 46)/(31 + 46)

                                                 = 0.429

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))

      = sqrt(0.429 * (1 - 0.429) * (1/31 + 1/46))

      = 0.115

At 99% confidence interval the critical value is z0.005 = 2.58

The 99% confidence interval is

(p1 - p2) +/- z0.005 * SE

= (0.387 - 0.457) +/- 2.58 * 0.115

= -0.07 +/- 0.297

= -0.367, 0.227

The interval cointains bothe positive and negative numbers i.e mixed.

WE are 99% confidence that the difference between the population proportion lies between this interval.

Option - 2 is correct.

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.