I had the following assignment and have completed the math. I am just unsure as to the answer for question C... is it because the 34% old favorable rate does not fall between the 95% confidence interval of 0.213 to 0.266) Here is the problem and the answers I came up with. I am unsure on the final question.

Has Gold Lost its Luster?

In 2011, when the Gallup organization polled a random sample of investors, 34% rated gold the best long-term investment. However, in April of 2013 Gallup surveyed another random sample of investors. Respondents were asked to select the best long-term investment from a list of possibilities. Only 241 of the 1005 respondents chose gold as the best long-term investment.

• Compute the standard error of the sample proportion. The standard error of the sample proportion is 0.0135.

SE ) =

Possible Changes (x) = 241

Sample Size (n) = 1005

Sample Proportion ( ) = = x/n

= 241/1005

= 0.2398

Standard Error = SQRT ((0.2398*(1-0.2398)/1005)) = 0.0135

SE ) = 0.0135

• Compute and describe a 95% confidence interval in the context of the case.The 95% confidence interval in the context of this case is (0.213,0.266)

p = + 1.96 x SEs

p = 0.2398 + 1.96 x SEs

p = 0.2398 + 1.96 x 0.0135

p = 0.2663

p = - 1.96 x SEs

p = 0.2398 - 1.96 x SEs

p = 0.2398 - 1.96 x 0.0135

p = 0.2133

Do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorable rate, or do you think this is a sample variability? Explain your answer using the calculated statistics.