The Consumer Reports National Research Center conducted a telephone survey of 2,

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 1,620 of the respondents think the future health of Social Security is a major economic concern.

If computing the confidence intervals manually, make sure to use at least three decimal digits for the critical values.

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 4 decimals)?

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).

( ,  )

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

Explanation / Answer

let point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern=p

then p=1620/2000=0.81 here sample size=n=2000

the SE(p)=sqrt(p(1-p)/n)=sqrt(0.81*(1-0.81)/2000)=0.0088

(a) required answer p=0.81

(b) with (1-alpha)*100% confidence the margin of error=z(alpha/2)*SE(p)

90% confidence the margin of error=z(0.1/2)*0.0088=1.6449*0.0088=0.0145

(c) (1-alpha)*100% confidence interval for proportion p=p± z(alpha/2)*SE(p)

90% confidence interval for p=0.81±z(0.1/2)*0.008=0.81±1.6449*0.0088=0.81±0.0145=(0.7955, 0.8245)

(d) (1-alpha)*100% confidence interval for proportion p=p± z(alpha/2)*SE(p)

95% confidence interval for p=0.81±z(0.05/2)*0.008=0.81±1.96*0.0088=0.81±0.0172=(0.7928, 0.8272)

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