A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98 % confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.
A) $0.316

Question

A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the  98 %  confidence interval for the true population proportion of all New York State union members who favor the Republican candidate.
A) $0.316 < p < 0.430$
B) $0.301 < p < 0.445$
C) $0.308 < p < 0.438$
D) $0.304 < p < 0.442$

Quizplus · Accepted Answer

The sample proportion is 112/300 = 0.373. Using the formula for a confidence interval for a proportion and a Z-score for 98% confidence (approximately 2.33), the interval is calculated as 0.373 ± 2.33 * sqrt((0.373*(1-0.373))/300), which results in the interval 0.308 to 0.438.

A Survey of 300 Union Members in New York State 0.316<p<0.4300.316 < p < 0.4300.316<p<0.430

A Survey of 300 Union Members in New York State $0.316 < p < 0.430$