When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 352352 of 11951195 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) The point estimate of the proportion of the population who would answer yes is 0.295.

(b) The margin of error for a 95% confidence interval is 0.0259.

(c) 95% confidence interval for population proportion is [0.2691 , 0.3209].

Step-by-step explanation:

We are given that a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 352 of 1195 subjects said yes.

Let = sample proportion of subjects who said yes.

(a) The point estimate of the proportion of the population who would answer yes = =  

So,    = 0.295

(b) Margin of error is given by =  

where, = level of significance = 1 - 0.95 = 5%

At 5% level of significance, z table gives critical value of 1.96 for two-sided interval.

Standard of error =   =    = 0.0132

So, Margin of error for 95% confidence interval =

                                                                               = 0.0259

(c) 95% confidence interval for population proportion is given by =

                   Point estimate Margin of error

              ⇒ 0.295 0.0259

              ⇒ [0.295 - 0.0259 , 0.295 + 0.0259]

              ⇒ [0.2691 , 0.3209]

So, 95% confidence interval = [0.2691 , 0.3209]

The numbers in this interval represent that we are 95% confident that the population proportion will lie between 0.2691 and 0.3209.

(d) Assumptions needed for constructing a confidence interval are;

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>