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 $.30.$

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.

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was five minutes. Use that as a planning value for the standard deviation in answering the following questions. a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 72 seconds, what sample size should be used? Assume 95% confidence. b. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

If the coefficient of variation is $40\%$ and the mean is $70$, then the variance is __.

In some reports, the mean and coefficient of variation are given. For instance, in Statistical Abstract of the United States, 116th Edition, one report gives the average number of physician visits by males per year. The average reported is 2.2, and the reported coefficient of variation is 1.5$\%$. Use this information to determine the standard deviation of the annual number of visits to physicians made by males?

It has been reported that $18.3 \%$ of all U.S. households were heated by electricity in 1980, compared to $27.4 \%$ in 1995 and $31.5 \%$ in 2005 . At the $0.05$ level, and assuming a sample size of 1000 U.S. households for each year, test whether the population percentages could be equal for these years. Source: Statistical Abstract of the United States 1996, p. 722; Statistical Abstract of the United States $2009, p. 610.$

A survey conducted by the American Automobile Association showed that a family of four spends an average of $\$215.60$ per day while on vacation. Suppose a sample of $64$ families of four vacationing at Niagara Falls resulted in a sample mean of $\$252.45$ per day and a sample standard deviation of $\$74.50.$

Develop a $95\%$ confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls.

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 .

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.

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?

What is the $95 \%$ confidence interval for the proportion of smokers in the population?

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.

Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint. 93 34 40 106 82 53 55 48 40 75 48 96 94 75 74 77 90 101 56 83 Assuming the population is roughly symmetric, construct a 95$ to $ per visit

A simple random sample of $60$ items resulted in a sample mean of $80.$ The population standard deviation is $\sigma= 15.$ Compute the $95\%$ confidence interval for the population mean.

A market research firm conducts telephone surveys with a $40\%$ historical response rate. What is the probability that in a new sample of $400$ telephone numbers, at least $150$ individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least $150/400 = .375$?

The Pew Research Center Internet Project, performed on the 25th anniversary of the Internet, involved a survey of 857 Internet users. It provided a variety of statistics on Internet users. For instance, in $2014,87 \%$ of American adults were Internet users. In 1995 only $14 \%$ of American adults used the Internet.

a. The sample survey showed that $90 \%$ of respondents said the Internet has been a good thing for them personally. Develop a $95 \%$ confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally.

The National Center for Education Statistics reported that $47\%$ of college students work to pay for tuition and living expenses. Assume that a sample of $450$ college students was used in the study.

Provide a $95\%$ confidence interval for the population proportion of college students who work to pay for tuition and living expenses.

The $92$ million Americans of age $50$ and over control $50$ percent of all discretionary income ($AARP~ Bulletin$, March $2008$). AARP estimated that the average annual expenditure on restaurants and carryout food was $\$1873$ for individuals in this age group. Suppose this estimate is based on a sample of $80$ persons and that the sample standard deviation is $\$550.$

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

b. What is the $95\%$ confidence interval for the population mean amount spent on restaurants and carryout food?

c. What is your estimate of the total amount spent by Americans of age $50$ and over on restaurants and carryout food?

d. If the amount spent on restaurants and carryout food is skewed to the right, would you expect the median amount spent to be greater or less than $\$1873$?