Workers in several industries were surveyed to determine the proportion of workers who feel their industry is understaffed. In the government sector, 37% of the respondents said they were understaffed, in the healthcare sector 33% said they were understaffed, and in the education sector, 28% said they were understaffed (USA Today, January 11, 2010). Suppose that 200 workers were surveyed in each industry. a. Construct a 95% confidence interval for the proportion of workers in each of these industries who feel their industry is understaffed.

A well-known bank credit card firm wishes to estimate the proportion of credit card holders who carry a nonzero balance at the end of the month and incur an interest charge. Assume that the desired margin of error is $.03$ at $98\%$ confidence.

How large a sample should be selected if no planning value for the proportion could be specified?

For a $t$ distribution with $16$ degrees of freedom, find the area, or probability, in each region.

Between $-2.120$ and $2.120$

For a $t$ distribution with $16$ degrees of freedom, find the area, or probability, in each region.

To the left of $1.337$

For a $t$ distribution with $16$ degrees of freedom, find the area, or probability, in each region.

To the right of $2.583$

For a $t$ distribution with $16$ degrees of freedom, find the area, or probability, in each region.

Between $-1.746$ and $1.746$

For a $t$ distribution with $16$ degrees of freedom, find the area, or probability, in each region.

To the left of $-1.746$

The $2003 ~Statistical ~Abstract ~of ~the ~United ~States$ reported the percentage of people $18$ years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of $.30.$

Assume that the study uses your sample size recommendation in part (a) and finds $520$ smokers. What is the point estimate of the proportion of smokers in the population?

In $2014$, the Centers for Disease Control reported the percentage of people $18$ years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of $.30.$
a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of $.02?$ Use $95\%$ confidence.
b. Assume that the study uses your sample size recommendation in part (a) and finds $520$ smokers. What is the point estimate of the proportion of smokers in the population?
c. What is the $95\%$ confidence interval for the proportion of smokers in the population?

Construct a $95\%$ confidence interval for the proportion of likely voters in Ohio who rated the economy as poor.

Importance of Economy to Voters. A survey of 750 likely voters in Ohio was conducted by the Rasmussen Poll just prior to the general election. The state of the economy was thought to be an important determinant of how people would vote. Among other things, the survey found that 165 of the respondents rated the economy as good or excellent and 315 rated the economy as poor.

b. Construct a $95 \%$ confidence interval for the proportion of likely voters in Ohio who rated the economy as good or excellent.

Importance of Economy to Voters. A survey of 750 likely voters in Ohio was conducted by the Rasmussen Poll just prior to the general election. The state of the economy was thought to be an important determinant of how people would vote. Among other things, the survey found that 165 of the respondents rated the economy as good or excellent and 315 rated the economy as poor.

a. Develop a point estimate of the proportion of likely voters in Ohio who rated the economy as good or excellent.

The Pew Research Center has conducted extensive research on the young adult population (Pew Research website, November 6,2012 ). One finding was that 93% of adults aged 18 to 29 use the Internet. Another finding was that 21% of those aged 18 to 28 are married. Assume the sample size associated with both findings is 500.

a. Develop a 95% confidence interval for the proportion of adults aged 18 to 29 who use the Internet.

b. Develop a 99% confidence interval for the proportion of adults aged 18 to 28 who are married.

c. In which case, part (a) or part (b), is the margin of error larger? Explain why.

A USA Today/CNN/Gallup survey of 369 working parents found 200 who said they spend too little time with their children because of work commitments.

What is the point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments?

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

What is the $95 \%$ confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments?