Question

When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the​ environment, 324 of 1140 subjects said yes.

a. Find the point estimate of the proportion of the population who would answer yes. (round to 6 decimal places)

b.Find the margin of error for a​ 95% confidence interval. (round to 6 decimal places)

c. Construct the​ 95% confidence interval for the population proportion. What do the numbers in this interval​ represent? (round to 6 decimal places)

d. State and check the assumptions needed for the interval in ​(c) to be valid. (round to 6 decimal places)

Answer 1

Answer: Given that, Sample size: 0.324 a) The point estimate of the proportion of the population who answer key - 324/1140 30.284211 b) sample pooportion, Ñ -02842 Standard ermori SE = { $x (1-P) / JO 284211*(1-0 2842040 SE -0.013358 95% CI is, arbo.o.95,2=1-0.95 = 0.05, 2/2=0.025, Zd/2=1.96 margin of error, ME = Zd2 * SE - 1-96*0.013358 (ME=0.026 182 ( 95%CI = Ê & ME -0.284211+0.026182 - O 28421-0.026182,0284211 +0.026182) :95%CI = 0.258029, 0.310393) d) the sample must be reasonably random the sample must be less than 10% of the population. the sample must be loge enough so that n r 10 & n(1-P) 210 for a confidence interval - Thank you