Question

In 2011, when the Gallup organization polled investors, 34% rated gold the best long-term investment. 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. By contrast, only 91 chose bonds.

1. Compute the standard error for each sample proportion. Compute and describe a 95% confidence interval in the context of the question.
2. Do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.
3. Suppose we want to increase the margin of error to 3%, what is the necessary sample size?
4. Based on the sample size obtained in part c, suppose 120 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.
5. 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 34% favorability rate, or do you think this is just sample variability? Explain.

(Please show calculations especially if formatted via excel)

Answer 1

Answer:

Formulas:

Given	population poroportion p0 =	0.34
	number of trails n=	1005
	Number of respondents for gold x=	241
	sample proportion p=	=C4/C3
a)	Standard error	=SQRT(C5*(1-C5)/C3)
	Confidence level =	0.95
	level of significance alpha =	=1-C9
	confidence interval =
	Lower limit	=C5-ABS(NORM.INV(C10/2,0,1))*C8
	Upper Limit	=C5+ABS(NORM.INV(C10/2,0,1))*C8
	Explanation:-	we are 95% confident that the proportion investors in gold is in between(0.213 , 0.266)
b)	Yes the opnions have changed significantly because the population proportion does not exist in the 95% CI
c)	Margin of error E =	0.03
	required Sample size n=	=ROUND(((NORM.INV(C10/2,0,1)/C18))^2*C2*(1-C2),0)
d)	number of trails n=	=C20
	Number of respondents for gold x=	120
	sample proportion p=	=C23/C22
	Standard error	=SQRT(C24*(1-C24)/C22)
	Confidence level =	0.95
	level of significance alpha =	=1-C28
	confidence interval =
	Lower limit	=C24-ABS(NORM.INV(C29/2,0,1))*C27
	Upper Limit	=C24+ABS(NORM.INV(C29/2,0,1))*C27
	Explanation:-	we are 95% confident that the proportion investors in gold is in between(0.104 , 0.146)
e	Yes the opnions have changed significantly because the population proportion does not exist in the 95% CI