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mathematics
statistics

Questions and Answers of Statistics

Morningstar publishes ratings data on 1208 company stocks (Morningstar website, October 24, 2012). A sample of 40 of these stocks is contained in the data set Morningstar. Use the data set to answer
The National Football League (NFL) polls fans to develop a rating for each football game (NFL website, October 24, 2012). Each game is rated on a scale from 0 (forgettable) to100 (memorable). The fan
One of the questions in the Pew Internet & American Life Project asked adults if they used the Internet, at least occasionally (Pew website, October 23, 2012). The results showed that 454 out of
A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample means x will be used to estimate the population mean.a. What is the expected value of
A sample of size 100 is selected from a population with p = .40.a. What is the expected value of ṕ?b. What is the standard error of ṕ?c. Show the sampling distribution of ṕ.d. What does the
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
Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe
A sample of 426 U.S. adults age 50 and older were asked how important a variety of issues were in choosing for whom to vote in the 2012 presidential election (AARP B, March 2012). a. What is the
Assume the population standard deviation is σ = 25. Compute the standard error of the mean, σx, for sample sizes of 50, 100, 150, and 200. What can you say about the size of the standard error of
Suppose a random sample of size 50 is selected from a population with σ = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction
Refer to the EAI sampling problem. Suppose a simple random sample of 60 employees is used.a. Sketch the sampling distribution of x when simple random samples of size 60 are used.b. What happens to
Barron’s reported that the average number of weeks an individual is unemployed is 17.5 weeks (Barron’s, February 18, 2008). Assume that for the population of all unemployed individuals the
The College Board reported the following mean scores for the three parts of the SAT (The World Almanac, 2009):Critical Reading ........502Mathematics ..........515Writing ............494Assume that
For the year 2010, 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return (The Wall Street Journal, October 25, 2012). The
The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches (Current Results website, October 27, 2012). Assume that the
The mean preparation fee H&R Block charged retail customers last year was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume the population standard
To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.a. Would you use the finite population correction factor in calculating the standard
Assume that the population proportion is .55. Compute the standard error of the proportion, σṕ, for sample sizes of 100, 200, 500, and 1000. What can you say about the size of the standard error
The population proportion is .30. What is the probability that a sample proportion will be within ± .04 of the population proportion for each of the following sample sizes?a. n = 100b. n = 200c. n =
The Wall Street Journal reported that the age at first startup for 55% of entrepreneurs was 29 years of age or less and the age at first startup for 45% of entrepreneurs was 30 years of age or more
People end up tossing 12% of what they buy at the grocery store (Reader’s Digest. March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery
Forty-two percent of primary care doctors think their patients receive unnecessary medical care (Reader’s Digest, December 2011/January 2012).a. Suppose a sample of 300 primary care doctors were
In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they
The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion is p = .76 and a sample of 400 consumers is
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from
U.S. News & World Report publishes comprehensive information on America’s best colleges (America’s Best Colleges, 2009 ed.). Among other things, they provide a listing of their 133 best national
The latest available data showed health expenditures were $8,086 per person in the United States or 17.6% of gross domestic product (Centers for Medicare & Medicaid Services website, April 1,
Foot Locker uses sales per square foot as a measure of store productivity. Sales are currently running at an annual rate of $406 per square foot (The Wall Street Journal, March 7, 2012). You have
Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and in-flight beverages. These additional charges average
After deducting grants based on need, the average cost to attend the University Of Southern California (USC) is $27,175 (U.S. News & World Report, America’s Best Colleges, 2009 ed.). Assume the
Three firms carry inventories that differ in size. Firm A’s inventory contains 2000 items, firm B’s inventory contains 5000 items, and firm C’s inventory contains 10,000 items. The population
A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500.a. How large was the sample used in this survey?b. What is the
A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x. If
Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website,
Advertisers contract with Internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click
The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15.a. Show the sampling distribution of ṕ
Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 25% of her sales calls. Viewing her sales calls for one
A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is σ = 5.a. What is the standard error of the mean, σx?b. At 95% confidence, what is the margin
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ = 15.a. Compute the 95% confidence interval for the population mean.b. Assume that the same
A 95% confidence interval for a population mean was reported to be 152 to 160. If σ = 15, what sample size was used in this study?
Data were collected on the amount spent by 64 customers for lunch at a major Houston restaurant. These data are contained in the file named Houston. Based on past studies the population standard
In an attempt to assess total daily travel taxes in various cities, the Global Business Travel Association conducted a study of daily travel taxes on lodging, rental cars, and meals (GBTA Foundation
Studies show that massage therapy has a variety of health benefits and it is not too expensive (The Wall Street Journal, March 13, 2012). A sample of 10 typical one-hour massage therapy sessions
AARP reported on a study conducted to learn how long it takes individuals to prepare their federal income tax return (AARP Bulletin, April 2008). The data contained in the file named TaxReturn are
For a t distribution with 16 degrees of freedom, find the area, or probability, in each region.a. To the right of 2.120b. To the left of 1.337c. To the left of – 1.746d. To the right of 2.583e.
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample
Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job contained in
Is your favorite TV program often interrupted by advertising? CNBC presented statistics on the average number of programming minutes in a half-hour sitcom (CNBC, February 23, 2006). The following
Consumption of alcoholic beverages by young women of drinking age in the United Kingdom, the United States, and Europe was reported (The Wall Street Journal, February 15, 2006). Data (annual
How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40.
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
There has been a trend toward less driving in the last few years, especially by young people. From 2001 to 2009 the annual vehicle miles traveled by people from 16 to 34 years of age decreased from
A simple random sample of 800 elements generates a sample proportion ṕ = .70.a. Provide a 90% confidence interval for the population proportion.b. Provide a 95% confidence interval for the
In a survey, the planning value for the population proportion is p* = .35. How large a sample should be taken to provide a 95% confidence interval with a margin of error of .05?
At 95% confidence, how large a sample should be taken to obtain a margin of error of .03 for the estimation of a population proportion? Assume that past data are not available for developing a
According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance (CNBC, February 23, 2006). Sample results, consistent with the CNBC reports showed 46 of
For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger
A sample survey of 54 discount brokers showed that the mean price charged for a trade of100 shares at $50 per share was $33.77 (AAII Journal, February 2006). The survey is conducted annually. With
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
In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of
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.a.
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.a. What is the point estimate of the proportion of
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
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
The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (The Wall Street Journal, March 5, 2008). The average cost per person for crashes in the Tampa,
Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3,486 (The Wall Street Journal
The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5.a. What is the point estimate of the population mean?b. What is the point estimate of the population standard
A simple random sample with n = 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4.a. Develop a 90% confidence interval for the population mean.b. Develop a 95% confidence
A sample containing years to maturity and yield for 40 corporate bonds is contained in the data file named CorporateBonds (Barron’s, April 2, 2012).a. What is the sample mean years to maturity for
The average cost per night of a hotel room in New York City is $273 (Smart Money, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.a.
Disney's Hannah Montana: The Movie opened on Easter weekend in April 2009. Over the three-day weekend, the movie became the number-one box office attraction (The Wall Street Journal, April 13, 2009).
The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.94 (US EIA website, April 6, 2012). The US EIA updates its estimates of
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the
An online survey by ShareBuilder, a retirement plan provider, and Harris Interactive reported that 60% of female business owners are not confident they are saving enough for retirement (SmallBiz,
One of the questions on a survey of 1000 adults asked if today’s children will be better off than their parents (Rasmussen Reports website October 26, 2012). Representative data are shown in the
According to Thomson Financial, through January 25, 2006, the majority of companies reported profits had beaten estimates (BusinessWeek, February 6, 2006). A sample of 162 companies showed 104 beat
Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver’s license. Twenty-five years later that percentage had dropped to 75% (University of Michigan Transportation Research
A poll for the presidential campaign sampled 491 potential voters in June. A primary purpose of the poll was to obtain an estimate of the proportion of potential voters who favored each candidate.
A Phoenix Wealth Management/Harris Interactive survey of 1500 individuals with net worth of $1 million or more provided a variety of statistics on wealthy people (BusinessWeek, September 22, 2003).
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
Russia has recently started a push for stronger smoking regulations, much like those in Western countries, concerning cigarette advertising, smoking in public places, and so on. The webfile named
The Health Care Cost Institute tracks health care expenditures for beneficiaries under the age of 65 who are covered by employer-sponsored private health insurance (Health Care Cost Institute
A recent article reported that there are approximately 11 minutes of actual playing time in a typical National Football League (NFL) game (The Wall Street Journal, January 15, 2010). The article
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.
A survey of 750 likely voters in Ohio was conducted by the Rasmussen Poll just prior to the general election (Rasmussen Reports website November 4, 2012). The state of the economy was thought to be
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
Although airline schedules and cost are important factors for business travelers when choosing an airline carrier, a USA today survey found that business travelers list an air-line’s frequent flyer
1. Develop appropriate descriptive statistics to summarize the data.2. Develop 95% confidence intervals for the mean age and household income of subscribers.3. Develop 95% confidence intervals for
1. Use appropriate descriptive statistics to summarize each of the three variables for the 40 Gulf View condominiums.2. Use appropriate descriptive statistics to summarize each of the three
1. Use appropriate descriptive statistics to summarize the transmission failure data.2. Develop a 95% confidence interval for the mean number of miles driven until transmission failure for the
The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a week end is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills
The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a
A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether
Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented.
The label on a 3-quart container of orange juice states that the orange juice contains an average of 1 gram of fat or less. Answer the following questions for a hypothesis test that could be used to
Carpetland salespersons average $8,000 per week in sales. Steve Contois, the firm’s vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial
Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour.a. State the appropriate null and
Consider the following hypothesis test:H0: μ ≥ 20Ha: μ < 20A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.a. Compute the value of the test statistic.b.
The Internal Revenue Service (IRS) provides a toll-free help line for taxpayers to call in and get answers to questions as they prepare their tax returns. In recent years, the IRS has been inundated

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