Question

Case Study One

Has Gold Lost Its Luster?

Please use ONLY one Excel file to complete the case study and upload the Excel file to the submission link (Week 3 Case Study) for grading. Please clearly mark your answers (either highlight or font colors) and grammar counts.

No credit will be granted for problems that are not completed using Excel.

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.

Answer 1

Excel formula

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