In 2011, when the Gallup organization polled investors, 30% 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 219 of the 875 respondents chose gold as the best long-term investment. By contrast, only 84 chose bonds.
a. Compute the standard error for each sample proportion. Compute and describe a 95% 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 30% favorability rate, or do you think this is just sample variability? Explain.
c. Suppose we want to increase the margin of error to 4%, what is the necessary sample size?
d. Based on the sample size obtained in part c, suppose 173 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 95% 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 30% favorability rate, or do you think this is just sample variability? Explain.
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