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 85 people were asked the voter registration question face to face. Of those sampled, seventy-three 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.

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 95% confidence interval for p1 – p2. (Use 3 decimal places.)

Lower Limit =

Upper Limit =

Answer 1

The statistic software output for this problem is :

Two sample proportion summary confidence interval:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions

95% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L=. Limit	U. Limit
p1 - p2	73	85	69	82	0.017360115	0.055256514	-0.090940663	0.12566089

Lower limit = -0.091

Upper limit = 0.126