Answer:
(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 = <u><em>sample proportion of subjects who said yes.</em></u>
(a) The point estimate of the proportion of the population who would answer yes = =
So, = <u>0.295</u>
(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 =
= <u>0.0259</u>
(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;
- The data must be sampled randomly.
- Sample values must be independent of each other.
- Data must follow normal distribution.