When the 2000 GSS asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 344 of 1170 subjects said yes.Use 3 decimal places. (a) What is the estimate of the population proportion who would answer yes?(b) What is the margin of error for this estimate? (Assume a 95% confidence level.)(c) Find a 95% confidence interval for the population proportion.(d) Which of the following assumptions are needed for the interval in (c) to be valid?

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Asked Mar 23, 2020
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When the 2000 GSS asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 344 of 1170 subjects said yes.

Use 3 decimal places. (a) What is the estimate of the population proportion who would answer yes?

(b) What is the margin of error for this estimate? (Assume a 95% confidence level.)

(c) Find a 95% confidence interval for the population proportion.
(d) Which of the following assumptions are needed for the interval in (c) to be valid?

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Expert Answer

Step 1

Hi! Thank you for posting the question. Since your question has more than three sub-parts, we have solved the first three sub-parts for you. If you need help with any other parts, please re-post the question and mention the part you need help with.

Here, n=1,170 subjects and the number of respondents who said “yes” is 344.

a.

The estimate of the population proportion will be obtained as given below:

Statistics homework question answer, step 1, image 1

Step 2

Margin of error (E):

The margin of error for proportion p is given by,

Statistics homework question answer, step 2, image 1

b.

Computing the margin of error for population proportion:

The confidence level is 95%. Therefore, the significance level, α = 0.05 and the z value corresponding to α/2 is 1.96.  The margin of error for population proportion is given by:

Statistics homework question answer, step 2, image 2

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