The start of the twenty-first century saw many corporate scandals and many indiv

Question

The start of the twenty-first century saw many corporate scandals and many individuals losing faith in business. In a 2007 poll conducted by the New York City-based Edelman Public Relations firm, 57% of respondents say they trust business to “do what is right.” This percentage was the highest in the annual survey since 2001.

a. If the sample size is 100, construct a 95% confidence interval estimate of the population proportion of individuals who trust business to “do what is right.”

b. If the sample size is 200, construct a 95% confidence interval estimate of the population proportion of individuals who trust business to “do what is right.”

c. Based on the results of part (a), can you conclude that more than half of the respondents trust business to “do what is right”? Explain your answer.

d. Based on the results of part (b), can you conclude that more than half of the respondents trust business to “do what is right”? Explain your answer.

e. Discuss the effect that sample size has on the width of confidence intervals.

Explanation / Answer

Formula for 95% confidence interval (CI) is P +/- 1.96 sqrt(p(1-p)/n) a) 0.57 +/- 1.96 sqrt((.57*.43)/100)= (.473, .667) b) 0.57+/- 1.96sqrt((.57*.43)/200) = (.501, .639) c) no because part of the CI falls below .5 d) yes, because no part of the CI falls below .5 e) Everything else equal, the larger the sample size, the smaller the width of the CI

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