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 1,640 of the respondents think the future health of Social Security is a major economic concern.

What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern (to 2 decimals)?
At 90% confidence, what is the margin of error (to 4 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 4 decimals).

Explanation / Answer

  a. The point estimate of the population proportion is simply the total number divided by the respondents:
1640/2000 = 0.82

b. Margin of error is the right size of the equation. What equation? This one: Za/2 sqrt(p-bar(1-pxbar)/n)

Plugging in your numbers looks like [1.645]]*[sqrt((.82)*(1-0.82)/2000))] (remember the 1.645 is in a table, probably located in your textbook) SOLVE, and you have Answer: 0.0141

c. Now we throw in the left side of the equation, plus and minus, the right size of the equation is just the estimate you had in letter a, 0.82. So plug that in and you have 0.82+[1.645]*[sqrt((0.82)*(1-0.82)/2000))] which leaves you with 0.834, then you have [1.96]*[sqrt((0.82)*(1-0.82)/2000))], which leaves you with the answer of 0.806 Answer: 0.8341 , 0.8058

d. You basically do what you do in letter c but you need a 95% confidence level, which is 1.96, so therefore you new equation will look like 0.82+[1.96]*[sqrt((0.82)*(1-0.82)/2000))] and 0.82-[1.96]*[sqrt((0.82)*(1-0.82)/2000))], Solve and your answer will be: 0.8032 , 0.8368

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