Question

Invest in science ~ The Pew Research Center conducted a survey of U.S. adults in 2019 to determine how American citizens feel about whether federal government should increase spending for scientific research. In the study, there were 711 Democrats and 647 Republicans. According to the survey, 436 Democrats and 270 Republicans said they are in favor of increased spending for scientific research.

We want to estimate the actual difference between the proportions of Democrats and Republicans who favor increased spending for scientific research.

Notation: 1=Democrats and 2=Republicans.

Based on this data, what is the upper bound for a 95% confidence interval for the difference in the population proportions, p1−p2

Answer 1

Here, , n1 = 711 , n2 = 647
p1cap = 0.6132 , p2cap = 0.4173

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.6132 * (1-0.6132)/711 + 0.4173*(1-0.4173)/647)
SE = 0.0266

For 0.95 CI, z-value = 1.96

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.6132 - 0.4173 - 1.96*0.0266, 0.6132 - 0.4173 + 1.96*0.0266)
CI = (0.1438 , 0.248)