Question

The Consumer Reports National Research Center conducted a telephone survey of 2,000 adults to learn about the major economic concerns for the future. The survey results showed that 1,660 of the respondents think the future health of Social Security is a major economic concern.

a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern?

b. At 90% confidence, what is the margin of error (to 3 decimals)? Use critical value with three decimal places.

c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern (to 3 decimals). Use critical value with three decimal places.

( ,  )

d. Develop a 95% confidence interval for this population proportion (to 3 decimals).

Answer 1

a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern?

point estimate=p^=x/n=1660/2000=0.83

he point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern is 0.83

b. At 90% confidence, what is the margin of error (to 3 decimals)? Use critical value with three decimal places.

margin of error=z*sqrt(p^*(1-p^)/n)

=1.645*sqrt(0.83*(1-0.83)/2000)

=0.01381702

margin of error=0.014

(rounding to 3 decimals)

. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern (to 3 decimals). Use critical value with three decimal places.

point estimate-margin of errot,point estimate +margin of error

0.83-0.01381702,0.83+0.01381702

0.816183,0.843817

0.816,0.844

ANSWER:

0.816,0.844

90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern lies in between 0.816,0.844

d. Develop a 95% confidence interval for this population proportion

zalpha/2 for 95%=1.96

0.83-1.96*sqrt(0.83*(1-0.83)/2000),0.83+1.96*sqrt(0.83*(1-0.83)/2000)

0.8135372,0.8464628

0.814,0.846

95% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern lies in between 0.814,0.846