Question

The election of a local construction union involves 2,000 union members. Among them, 500 members are randomly selected and asked whether they planned to vote for the incumbent Union President or the challenger. Of the 500 surveyed, 350 said they would vote for the incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the incumbent

Answer 1

Answer:

The 99% of confidence limits for the proportion that plan to vote for the incumbent.

(0.6473 ,0.7527)

Step-by-step explanation:

Explanation:-

Given data the election of a local construction union involves 2,000 union members. Among them, 500 members are randomly selected.

Given large sample size 'N' = 2000

Given sample size 'n' = 500

Given data Of the 500 surveyed, 350 said they would vote for the incumbent.

The sample Proportion

                        $p = \frac{x}{n} = \frac{350}{500} =0.7$

                       q = 1-p = 1 - 0.7 = 0.3

Confidence intervals:-

The 99% of confidence intervals are determined by

$(p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p+Z_{\alpha }\sqrt{\frac{pq}{n} } )$

The z- score of 0.99 level of significance =2.576

$(0.7-2.576\sqrt{\frac{0.7X0.3}{500} } , 0.7+2.576\sqrt{\frac{0.7X0.3}{500} } )$

on using calculator, we get

(0.7 - 0.0527 ,0.7+0.0527)

(0.6473 ,0.7527)

Conclusion:-

The 99% of confidence limits for the proportion that plan to vote for the incumbent.

(0.6473 ,0.7527)