Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-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

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-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) $0.304 < p < 0.442$
C) $0.301 < p < 0.445$
D) $0.308 < p < 0.438$

Quizplus · Accepted Answer

The sample proportion is 112/300 = 0.373. Using a 98% confidence level, the critical value (z-score) is approximately 2.33. The standard error is calculated as sqrt[(0.373)(1-0.373)/300]. The confidence interval is then 0.373 ± 2.33 * standard error, which results in the interval $0.308 < p < 0.438$.

Use the Given Degree of Confidence and Sample Data to Construct