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StatisticsQ&A LibraryWhen 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?Question

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?

Step 1

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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:

Step 2

**Margin of error (E):**

The margin of error for proportion *p *is given by,

**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:

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