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

8.3 Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 707 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? Appendix A Statistical Tables

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

___________ ≤ p ≤ __________

The point estimate is _______.

Expert Solution

Solution :

n =1255

x = 707

The point estimate is

= x / n = 707 / 1255 = 0.563

1 - = 1 - 0.563= 0.437

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 = 1.960

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

= 1.960 * ( $\sqrt$ ((0.563 * 0.437) / 1255)

= 0.027

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.563 - 0.027 < p < 0.563 + 0.027

0.536 < p < 0.590

milcah answered 1 year ago

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