A political candidate wants to estimate her chances of winning the coming election for mayor. Out...

A political candidate wants to estimate her chances of winning the coming election for mayor. Out of a random sample of 500 voters, 240 voters stated they supported the candidate. Find the 95% confidence interval for , the true proportion of supporters. p (a) (.42, .54) (b) (.44, .52) (c) (.46, .40) (d) (.47, .49) (e) (.38, .58)

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Expert Solution

solution:

Given that,

n = 500

x = 240

= x / n = 240 / 500.= 0.48

1 - = 1 - 0.48 = 0.52

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * ( $\sqrt$ ((0.48 * 0.52) / 500) = 0.04

A 95 % confidence interval for proportion p is ,

- E < P < + E

0.48 - 0.04 < p < 0.48 + 0.04

0.44 < p < 0.52

(0.44,0.52)

correct option (b)

orchestra answered 1 year ago

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