Question

In: Statistics and Probability

Is the environment a major issue with Americans? To answer that question, a researcher conducts a...

Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 730 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion?

(Round the intermediate values to 3 decimal places. Round your answer to 3 decimal places.)

enter the lower limit of the confidence interval ≤ p ≤ enter the upper limit of the confidence interval

The point estimate is enter the point estimate .

Expert Solution

Solution :

Given that,

Point estimate = sample proportion = = x / n = 730 / 1255 = 0.582

1 - = 1 - 0.582 = 0.418

Z_/2 = 1.96

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

= 1.96 * ( $\sqrt$ ((0.582 * 0.418) / 1255)

= 0.027

A 95% confidence interval for population proportion p is ,

- E p + E

0.582 - 0.027 p 0.582 + 0.027

0.555 p 0.609

The lower limit of the confidence interval 0.555 ≤ p ≤ 0.609 enter the upper limit of the confidence interval

orchestra answered 1 year ago

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