Question

Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below: UVA (Pop. 1):UNC (Pop. 2):n1=80,n2=99,p^1=0.736p^2=0.602 Find a 97.9% confidence interval for the difference p1−p2 of the population proportions. (Give your answer as two values inside parentheses, separated by a comma, and rounded to at least three decimal places. Do not round values in preliminary calculations.)

Answer 1

The statistical 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

97.9% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	58.88	80	59.598	99	0.134	0.069634486	-0.026715312	0.29471531

Hence,

97.9% confidence interval will be:

(-0.027, 0.295)