Question

In 2011, when the Gallup organization polled investors, 34% rated gold the best long-term investment. However, 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 241 of the 1005 respondents chose gold as the best long-term investment. Compute and describe a 95% confidence interval in the context of the case.

Answer 1

n= 1005, x= 241, C= 95%

formula for confidence interval is

Where Zc is the Z critical value for C= 95%

we can find critical value using normal z table

we get,

Zc= 1.96

0.2134 < P < 0.2662

Confidence interval for the proportion of respondents who chose gold as

the best long-term investment is (0.2134 ,  0.2662)

Interpretation :

Therefore we are 95% confident that the true proportion of respondents who

chose gold as the best long-term investment lies between (0.2134 ,  0.2662).