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. • 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.

Answer 1

Null and alternative hypotheses

Ho : p = 0.34

H1 : p   0.34

Level of significance a = 0.05

Test statistic

Z = p^ - p / S.E(p^)

Where p^ = 241/1005 = 0.240

S.E(p^) = sqrt(0.34*0.66/1005) = 0.0149

Z = 0.240 - 0.340/0.0149

Z = -6.69

Zcritical for a = 0.05 , Za/2 = Z0.025 = - 1.96

Decision rule : If Z < -1.96 , we reject the null hypothesis

Here Z = -6.69 < -1.96

Decision : we reject the null hypothesis

Conclusion : There is sufficient evidence the value of gold as a long term investment have really changed from old 34% favourable rate