(a) A poll of 2,277 likely voters was conducted on the president's performance. Approximately what margin...

(a) A poll of 2,277 likely voters was conducted on the president's performance. Approximately what margin of error would the approval rating estimate have if the confidence level is 95%? (Round your answer to 4 decimal places.)

Margin of error

(b) The poll showed that 44% approved the president's performance. Construct a 90% confidence interval for the true proportion. (Round your answer to 4 decimal places.)

The 90% confidence interval is from to .

Solutions

Expert Solution

Solution :

Given that,

a) Point estimate = sample proportion = = 0.44

1 - = 1 - 0.44

Z/2 = Z0.025 = 1.96

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

= 1.96 ( $\sqrt$ ((0.44 * 0.56) /2277 )

= 0.0204

b) Z/2 = Z0.05 = 1.645

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

= 1.645 ( $\sqrt$ ((0.44 * 0.56) /2277 )

= 0.0171

A 90% confidence interval for population proportion p is

± E

= 0.44 ± 0.0171

= ( 0.4229, 0.4571 )

orchestra answered 1 year ago

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