Question

A poll asked whether states should be allowed to conduct random drug tests on elected officials. Of 21 comma 438 21,438 ​respondents, 59​% said​ "yes." a. Determine the margin of error for a​ 99% confidence interval. b. Without doing any​ calculations, indicate whether the margin of error is larger or smaller for a​ 90% confidence interval. Explain your answer.

a. The margin of error for a​ 99% confidence interval is nothing . ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

a) n = 21438

Point estimate = sample proportion = = 0.59

1 - = 1- 0.59 = 0.41

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z0.005 = 2.576

Z/2 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576  * ((0.59*(0.41) /21438 )

= 0.009

b) smaller .

Increase the confidence level margin of error is decreased.

c)

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576  * ((0.59*(0.41) /21438 )

= 0.009