When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 328 of 1140 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.

d. -Sample selection was random

-Individual observations are independent of each other

np≥10

Step-by-step explanation:

a. The point estimate of a sample proportion is obtained using the formula;

Hence,  the point estimate of the proportion of the population is 0.2877

b. The desired margin of error is the calculated using the point estimate value as follows:

Hence, the desired margin of error for the sample proportion is 0.0263

c. Given a confidence level of 95%, the confidence interval can be calculated as:

Hence, the confidence interval at 95% confidence level is 0.2614<p<0.3140

#We are 95% confident that the interval estimate  contains the desired proportion.

d. The assumptions are:

-The sample size is is more than 10 or equal to 10:

-The selection was from a randomized experiment.

-The individual observations were independent of each other.