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 29 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 29 people interviewed face to face, 12 answered the question accurately. The second random sample consisted of 41people who had been charged with drunken driving. During a telephone interview, 23 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 μ, difference of means μ₁ – μ₂, or difference of proportions p₁ – p₂. Then solve the problem.

μ₁ – μ₂p     p₁ – p₂μ

(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.)

lower limit
upper limit

(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?

Because the interval contains only positive numbers, we can say that there is a higher proportion of accurate responses in face-to-face interviews.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.     We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of accurate responses in telephone interviews.

Answer 1

using excel>addin>phstat>two sample test

we have

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0		of the Difference Between Two Proportions
Level of Significance	0.05
Group 1			Data
Number of Items of Interest	12		Confidence Level	99%
Sample Size	29
Group 2			Intermediate Calculations
Number of Items of Interest	23		Z Value	-2.5758
Sample Size	41		Std. Error of the Diff. between two Proportions	0.1199
			Interval Half Width	0.3088
Intermediate Calculations
Group 1 Proportion	0.413793103		Confidence Interval
Group 2 Proportion	0.56097561		Interval Lower Limit	-0.4560
Difference in Two Proportions	-0.14718251		Interval Upper Limit	0.1616
Average Proportion	0.5000
Z Test Statistic	-1.2132
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.2251
Do not reject the null hypothesis

(a) difference of proportions p1 – p2. =-0.14718251

(b) a 99% confidence interval for p1 – p2.

Interval Lower Limit	-0.456
Interval Upper Limit	0.162

c) mixed

.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.