In: Statistics and Probability
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.)
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