Question

Please use ONLY one Excel file to complete case study one, and use one spreadsheet for each problem. No credit will be granted for problems that are not completed using Excel.

In 2011, when the Gallup organization polled investors, 32% rated gold the best long-term investment. But 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 168 of the 650 respondents chose gold as the best long-term investment. By contrast, only 83 chose bonds.

1. Compute the standard error for each sample proportion. Compute and describe a 99% 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 32% favorability rate, or do you think this is just sample variability? Explain.
3. Suppose we want to keep the margin of error at 4%, and we still want to construct a 99% confidence interval. What is the necessary sample size?
4. Based on the sample size obtained in part c, suppose 306 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 99% 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 32% favorability rate, or do you think this is just sample variability? Explain.

Answer 1

Ans ) In spreadsheet one

Confidence Interval Estimate for the Proportion
Data		Command used
Sample Size	650
Number of people choose gold	168
Confidence Level	99%
Intermediate Calculations
Sample Proportion	0.258461538	B5/B4
Z Value	-2.5758	NORM.S.INV((1-B6)/2)
Standard Error of the Proportion	0.0172	SQRT(B9*(1-B9)/B4)
Interval Half Width	0.0442	ABS(B10*B11)
Confidence Interval
Interval Lower Limit	0.2142	B9-B12
Interval Upper Limit	0.3027	B9+B12
a ) the standard error is 0.0172 and the 99% confidence interval is (0.2142,0.3027)
b ) yes the value of gold as long term investment have really changed from the old 32% favourablity rate because 0.32 is not in the interval given by option a )

In spreadsheet 2

Sample Size Determination
Data		Formula used
Estimate of True Proportion	0.2585
Sampling Error	0.04
Confidence Level	99%
Intermediate Calculations
Z Value	-2.5758	NORM.S.INV((1-B6)/2)
Calculated Sample Size	794.8513	(B9^2*B4*(1-B4))/B5^2
Result
Sample Size Needed	795.0000
c ) the necessary sample size needed is 795

In spreadsheet 3

Confidence Interval Estimate for the Proportion
Data		Command used
Sample Size	795
Number of Successes	306
Confidence Level	99%
Intermediate Calculations
Sample Proportion	0.38490566	B5/B4
Z Value	-2.5758	NORM.S.INV((1-B6)/2)
Standard Error of the Proportion	0.0173	SQRT(B9*(1-B9)/B4)
Interval Half Width	0.0445	ABS(B10*B11)
Confidence Interval
Interval Lower Limit	0.3405	B9-B12
Interval Upper Limit	0.4294	B9+B12
d ) the standard error is 0.0173 and the 99% confidece interval is (0.3405,0.4294)
e ) No, the value of gold as long term investment have not really changed from the old 32% favourablity rate because 0.32 is in the interval given by option d )