Question

A study considered the question, "Are you a registered voter?" Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a face-to-face interview and a telephone interview. A random sample of 95 people were asked the voter registration question face to face. Of those sampled, eighty respondents gave accurate answers (as verified by city records). Another random sample of 82 people were asked the same question during a telephone interview. Of those sampled, sixty-nine respondents gave accurate answers. Assume the samples are representative of the general population.

(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.

p₁ – p₂μ₁ – μ₂    μp

(b) 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 during a telephone interview. Find a 99% confidence interval for p₁ – p₂. (Use 3 decimal places.)

lower limit
upper limit

(c) 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 99% level, do you detect any difference in the proportion of accurate responses from face-to-face interviews 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.

Answer 1

Given:

n1 = 95 X1 = 80

n2 = 82 X2 = 69

a) p1 - p2

b) 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 during a telephone interview.

A 99% confidence interval for p₁ – p_{2 :}

_{Therefore 99% CI is (-0.141, 0.142)}

Lower limit = -0.141

Upper limit = 0.142

It is 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.

Answer - option 2