# Question: In June 2012 a Gallup Poll showed that when a

In June 2012, a Gallup Poll showed that when a sample of Americans were asked whether they were thriving, struggling, or suffering, about 54% said they were thriving.

a. Assuming the sample size was 1000, how many in the sample said they were thriving?

b. Is the sample size large enough to apply the Central Limit Theorem? Explain. Assume the other conditions are met.

c. Find a 95% confidence interval for the proportion that said they were thriving.

d. Find the width of the interval you found in part b by subtracting the lower limit from the upper limit. Round your answer to the nearest whole percent.

e. Now assume the sample size was 4000. How many would have said they were thriving?

f. Find a 95% confidence interval for the proportion that said they were thriving using the numbers from part e.

g. What is the width of the interval you found in part f?

h. When the sample size is multiplied by 4 (as it was here, going from 1000 to 4000), is the interval width decreased by a factor of 4? In other words, is the interval for the larger sample size one-fourth (1/4) of the interval for the smaller sample size? If not, what is it divided by?

a. Assuming the sample size was 1000, how many in the sample said they were thriving?

b. Is the sample size large enough to apply the Central Limit Theorem? Explain. Assume the other conditions are met.

c. Find a 95% confidence interval for the proportion that said they were thriving.

d. Find the width of the interval you found in part b by subtracting the lower limit from the upper limit. Round your answer to the nearest whole percent.

e. Now assume the sample size was 4000. How many would have said they were thriving?

f. Find a 95% confidence interval for the proportion that said they were thriving using the numbers from part e.

g. What is the width of the interval you found in part f?

h. When the sample size is multiplied by 4 (as it was here, going from 1000 to 4000), is the interval width decreased by a factor of 4? In other words, is the interval for the larger sample size one-fourth (1/4) of the interval for the smaller sample size? If not, what is it divided by?

## Relevant Questions

In May 2012, a Gallup Poll showed that 63% of randomly surveyed U.S. adults said the United States benefits from having a rich class. (The proportion was unchanged from 1990. The percentage was higher for Republicans than ...In the 2012 General Social Survey, people were asked their opinions on astrology—whether it was very scientific, somewhat scientific, or not at all scientific. Of 1974 who responded, 101 said astrology was very ...Refer to Exercise 7.67 for information. This data set records results just for the boys. a. Find and compare the percentages that graduated for each group, descriptively. Does this suggest that preschool was linked with a ...A July 2011 Roper Poll showed that 59% of its randomly selected U.S. adults would support banning smoking in all public places. (This was up from 44% in July 2010.) Suppose the margin of error was 4 percentage points with a ...Are the career goals of young women changing? A Pew Poll asked young women about the importance they place on having a high-paying career or profession. Those women who said being successful in a high-paying career is “one ...Post your question