Question

When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the​ environment, 354 of 1180 subjects said yes. a. Find the point estimate of the proportion of the population who would answer yes. b. Find the margin of error for a​ 95% confidence interval. c. Construct the​ 95% confidence interval for the population proportion. What do the numbers in this interval​ represent? d. State and check the assumptions needed for the interval in ​(c) to be valid.

a. Find the point estimate of the proportion of the population who would answer yes. ModifyingAbove p with caretequals ​(Round to five decimal places as​ needed.)

b. Find the margin of error for a​ 95% confidence interval. ​(Round to five decimal places as​ needed.)

c. Construct the​ 95% confidence interval for the population proportion. ​(Round to five decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 1180

x = 354

Point estimate = sample proportion = = x / n = 354 / 1180=0.3

1 - = 1 - 0.3=0.7

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 (((0.3*0.7) / 1180)

= 0.02615

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.3 - 0.02615< p < 0.3 + 0.02615

0.27385< p < 0.32615

0.27385,0.32615