In a survey of 1000 randomly selected adults in the United States, participants

Question

In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories! Math was chosen by 232 of the 1000 as the favorite subject, and it was also chosen by 372 of the 1000 as the least favorite subject.

(a) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the favorite subject in school. (Give the answers to four decimal places.)


(b) Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the least favorite subject. (Give the answers to four decimal places.)

You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

Confidence interval for population proportion is
sample proportion +/- confidence coefficient*standard error of p
a) Sample proportion = p = x/n = 232/1000 = 0.232
Confidence coefficient is the critical value of z for 95% confidence level = 1.96
Standard error of p = sqrt [p*(1-p)/n]
= sqrt [0.232*0.764/1000]
= 0.0133
Therefore, the CI required is
0.232 +/- 1.96*0.0133
0.232 +/- 0.0260
lower bound is 0.232 - 0.0260 = 0.206
upper bound is 0.232 + 0.0260 = 0.258
The CI required is [0.2097, 0.2623]

b) Sample proportion = p = x/n = 372/1000 = 0.372
The CI required is
0.372 +/- 1.96 * sqrt [0.372*0.62/1000]

0.372+/- 0.0152

lower bound is 0.372 - 0.0152 = 0.3568

upper bound is 0.372 + 0.0152= 0.3872
The CI required is [0.3568, 0.3872]

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.