In a recent poll of $760$ homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying off. Using a confidence coefficient of $0.90$, derive the interval estimate for the proportion of all homeowners in the United States that hold a home equity loan.

In a CNNMoney.com poll conducted on July 13, 2010, a sample of 5,324 Americans were asked about what matters most to them in a place to live. Thirty-seven percent of the respondents felt job opportunities matter most.

a. Construct the $90 \%$ confidence interval for the proportion of Americans who feel that good job opportunities matter most in a place to live.

b. Construct the $99 \%$ confidence interval for the proportion of Americans who feel that good job opportunities matter most in a place to live.

c. Which of the above two intervals has a higher margin of error? Explain why.

A survey of 1,026 people asked: "What would you do with an unexpected tax refund?" Fortyseven percent responded that they would pay off debts (Vanity Fair, June 2010).

a. At $95 \%$ confidence, what is the margin of error?

b. Construct the $95 \%$ confidence interval for the population proportion of people who would pay off debts with an unexpected tax refund.

A poll of 1,079 adults found that $51 \%$ of Americans support Arizona's stringent new immigration enforcement law, even though it may lead to racial profiling (The New York Times/CBS News, April 28-May 2, 2010). Use the sample information to compute the $95 \%$ confidence interval for the population parameter of interest.

In a sample of 30 observations, the number of successes equals 18.

a. Construct the $88 \%$ confidence interval for the population proportion of successes.

b. Construct the $98 \%$ confidence interval for the population proportion of successes.

c. What happens to the margin of error as you move from the $88 \%$ confidence interval to the $98 \%$ confidence interval?

A random sample of 100 observations results in 40 successes.

a. What is the point estimate for the population proportion of successes?

b. Construct $90 \%$ and $99 \%$ confidence intervals for the population proportion.

c. Can we conclude at $90 \%$ confidence that the population proportion differs from $0.5$ ?

d. Can we conclude at $99 \%$ confidence that the population proportion differs from $0.5$ ?