In a recent presidential election, 611 voters were surveyed and 308 of them said that they...

In a recent presidential election, 611 voters were surveyed and 308 of them said that they voted for the candidate who won. a) Find the point estimate of the percentage of voters who said that they voted for the candidate who won. b) Find a 98% confidence interval estimate of the percentage of voters who said that they voted for the candidate who won.

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Expert Solution

Solution :

Given that,

n = 611

x = 308

(a)

Point estimate = = x / n = 308 / 611 = 0.504

1 - = 1 - 0.504 = 0.496

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

Margin of error = E = Z_{/ 2} * $\sqrt$ (( * (1 - )) / n)

= 2.326 * ( $\sqrt$ ((0.504 * 0.496) / 611)

= 0.047

(b)

A 98% confidence interval for population proportion p is ,

- E < P < + E

0.504 - 0.047 < p < 0.504 + 0.047

0.457 < p < 0.551

(0.457 , 0.551)

orchestra answered 1 year ago

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