Question

Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 722 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:___

Answer 1

Solution :

Given that,

n = 1255

x = 722

Point estimate = sample proportion = = x / n =722/1255=0.575

1 - = 1 - 0.575=0.425

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96} ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )   

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.575*0.425) /1255 )

E = 0.027

A 95% confidence interval for population proportion p is ,

- E≤ p ≤ + E

0.575 - 0.027≤ p ≤0.575 + 0.027

0.548≤ p ≤0.602

The 95% confidence interval for the population proportion p is : 0.548≤ p ≤0.602