Question

n 2011, when the Gallup organization polled investors, 26% rated gold the best long-term investment. But in April of 2013 Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 189 of the 760 respondents chose gold as the best long-term investment. By contrast, only 87 chose bonds.

a. Compute the standard error for each sample proportion. Compute and describe a 90% confidence interval in the context of the question.

b. Do you think opinions about the value of gold as a long-term investment have really changed from the old 26% favorability rate, or do you think this is just sample variability? Explain.

c. Suppose we want to keep the margin of error at 3%, and we still want to construct a 90% confidence interval. What is the necessary sample size?

d. Based on the sample size obtained in part c, suppose 167 respondents chose gold as the best long-term investment. Compute the standard error for choosing gold as the best long-term investment. Compute and describe a 90% confidence interval in the context of the question.

e. Based on the results of part d, do you think opinions about the value of gold as a long-term investment have really changed from the old 26% favorability rate, or do you think this is just sample variability? Explain.

Answer 1