We are interested in conducting a study to determine the proportion of voters who would vote for the incumbent governor. A sample of 400 voters was taken, and 285 of these favored the incumbent.

Construct and explain a 90% confidence interval estimate of the proportion of all voters who support the incumbent.

Question

High School

Answer :

ShubhamChaurasia ShubhamChaurasia · Answer 1 · 2024-10-28T20:29:13-04:00

The 90% confident interval is (0.6754, 0.7496).

The formula for the confidence interval for a proportion in a population is as follows:

p ± z(α/2) * √[ (p * ( 1 - p) / n) ]

Here,

p = sample proportion

n = size of the sample

z(α/2) = critical value of the normal distribution at α/2 (significant level divided by 2).

The value of z(α/2) is obtained from the standard normal distribution tables.

For getting the Sample proportion we know the formula,

Sample proportion(p) = Favoring the incumbent / Total voters

p = 285/400

p = 0.7125

Critical value at 90% confidence interval = 1.645 (From the z-distribution table)

The Margin of Error (ME) is the range in which the true population proportion may lie. It can be calculated as follows:

ME = z * SE

(SE) = √[ p * ( 1 - p ) / n ]

SE = √ [(0.7125 * 0.2875) / 400] = 0.0226

ME = 1.645 * 0.0226

ME = 0.0371

Confidence Interval = Sample Proportion ± Margin of Error

CI = 0.7125 ± 0.0371

0.7496

CI = (0.6754, 0.7496)

Hence, the 90% confidence interval for the proportion of all voters who support the incumbent governor is(0.6754, 0.7496).

To know more about the "confidence interval": https://brainly.com/question/15712887

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