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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Refer to the Hudson Marine problem in exercise 53.a. Compute the centered moving average values for this time series.b. Construct a time series plot that also shows the centered moving average and
Refer to the Hudson Marine data in exercise 53.a. Deseasonalize the data and use the deseasonalized time series to identify the trend.b. Use the results of part (a) to develop a quarterly forecast
The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003). Sample
A company that manufactures toothpaste is studying five different package designs.Assuming that one design is just as likely to be selected by a consumer as any other design, what selection
Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice.a. How many sample points are possible? (Hint: Use the counting
Fortune magazine publishes an annual list of the 500 largest companies in the United States.The following data show the five states with the largest number of Fortune 500 companies(The New York Times
The U.S. adult population by age is as follows (The World Almanac, 2009). The data are in millions of people.Assume that a person will be randomly chosen from this population.a. What is the
Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A B C {E1, E2}{E3, E4}{E2, E3, E5}a. Find P(A), P(B), and P(C).b. Find P(A B). Are A and B
Suppose that we have a sample space S {E1, E2, E3, E4, E5, E6, E7}, where E1, E2,..., E7 denote the sample points. The following probability assignments apply: P(E1) .05, P(E2) .20, P(E3) .20, P(E4)
High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) .30 and P(B) .40.a. What is P(A B)?b. What is P(A B)?c. A student in statistics argues that
A Morgan Stanley Consumer Research Survey sampled men and women and asked each whether they preferred to drink plain bottled water or a sports drink such as Gatorade or Propel Fitness water (The
The prior probabilities for events A1, A2, and A3 are P(A1) .20, P(A2) .50, and P(A3).30. The conditional probabilities of event B given A1, A2, and A3 are P(B A1) .50, P(B A2) .40, and P(B A3)
Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities
Consider the experiment of a worker assembling a product.a. Define a random variable that represents the time in minutes required to assemble the product.b. What values may the random variable
In November the U.S. unemployment rate was 4.5% (USA Today, January 4, 2007). The Census Bureau includes nine states in the Northeast region. Assume that the random variable of interest is the number
The probability distribution for the random variable x follows.a. Is this probability distribution valid? Explain.b. What is the probability that x 30?c. What is the probability that x is less than
Nationally, 38% of fourth-graders cannot read an age-appropriate book. The following data show the number of children, by age, identified as learning disabled under special education. Most of these
The percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers are as follows. The scores range from a low of 1 (very
A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3.Let x be a random variable indicating the number of sessions required to gain
The following table is a partial probability distribution for the MRA Company’s projected profits (x profit in $1000s) for the first year of operation (the negative value denotes a loss).a. What is
The following table provides a probability distribution for the random variable x.a. Compute E(x), the expected value of x.b. Compute σ2 , the variance of x.c. Compute σ, the standard deviation of
The following table provides a probability distribution for the random variable y.a. Compute E( y).b. Compute Var( y) and σ.
The number of students taking the Scholastic Aptitude Test (SAT) has risen to an all-time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in
The American Housing Survey reported the following data on the number of bedrooms in owner-occupied and renter-occupied houses in central cities (U.S. Census Bureau website, March 31, 2003).a. Define
The National Basketball Association (NBA) records a variety of statistics for each team.Two of these statistics are the percentage of field goals made by the team and the percentage of three-point
The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.a. Use the expected collision payment to determine the collision
Consider a binomial experiment with two trials and p .4.a. Draw a tree diagram for this experiment (see Figure 5.3).b. Compute the probability of one success, f(1).c. Compute f(0).d. Compute f(2).e.
Consider a binomial experiment with n 20 and p .70.a. Compute f(12).b. Compute f(16).c. Compute P(x 16).d. Compute P(x 15).e. Compute E(x).f. Compute Var(x) and σ.Applications
A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.a. Compute the probability that two or
Consider a Poisson distribution with a mean of two occurrences per time period.a. Write the appropriate Poisson probability function.b. What is the expected number of occurrences in three time
More than 50 million guests stay at bed and breakfasts (B&Bs) each year. The website for the Bed and Breakfast Inns of North America, which averages seven visitors per minute, enables many B&Bs to
Suppose N 15 and r 4.What is the probability of x 3 for n 10?Applications
Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in Las Vegas casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) and tens have a point
Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 40 employees; the Hawaii plant has
A random sample of 10 employees is to be asked to fill out a benefits questionnaire.a. What is the probability that none of the employees in the sample work at the plant in Hawaii?b. What is the
The Troubled Asset Relief Program (TARP), passed by the U.S. Congress in October 2008, provided $700 billion in assistance for the struggling U.S. economy. Over $200 billion was given to troubled
The American Association of Individual Investors publishes an annual guide to the top mutual funds (The Individual Investor’s Guide to the Top Mutual Funds, 22e, American Association of Individual
A survey showed that the average commuter spends about 26 minutes on a one-way doorto-door trip from home to work. In addition, 5% of commuters reported a one-way commute of more than one hour
A regional director responsible for business development in the state of Pennsylvania is concerned about the number of small business failures. If the mean number of small business failures per month
The random variable x is known to be uniformly distributed between 10 and 20.a. Show the graph of the probability density function.b. Compute P(x 15).c. Compute P(12 x 18).d. Compute E(x).e.
Most computer languages include a function that can be used to generate random numbers.In Excel, the RAND function can be used to generate random numbers between 0 and 1.If we let x denote a random
Given that z is a standard normal random variable, find z for each situation.a. The area to the right of z is .01.b. The area to the right of z is .025.c. The area to the right of z is .05.d. The
A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society (U.S. Airways Attaché, September 2000). If IQ scores are
Trading volume on the New York Stock Exchange is heaviest during the first half hour(early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions
Assume a binomial probability distribution has p .60 and n 200.a. What are the mean and standard deviation?b. Is this situation one in which binomial probabilities can be approximated by the normal
Consider the following exponential probability density function.a. Find P(x 6).b. Find P(x 4).c. Find P(x 6).d. Find P(4 x 6).
Consider the following exponential probability density function.a. Write the formula for P(x x0).b. Find P(x 2).c. Find P(x 3).d. Find P(x 5).e. Find P(2 x 5).Applications
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.a. Sketch this exponential probability distribution.b.
The U.S. Bureau of Labor Statistics reports that the average annual expenditure on food and drink for all families is $5700 (Money, December 2003). Assume that annual expenditure on food and drink is
The website for the Bed and Breakfast Inns of North America gets approximately seven visitors per minute (Time, September 2001). Suppose the number of website visitors per minute follows a Poisson
The time (in minutes) between telephone calls at an insurance claims office has the following exponential probability distribution.a. What is the mean time between telephone calls?b. What is the
Assume a finite population has 350 elements. Using the last three digits of each of the following five-digit random numbers (e.g., 601, 022, 448, . . . ), determine the first four elements that will
Fortune publishes data on sales, profits, assets, stockholders’ equity, market value, and earnings per share for the 500 largest U.S. industrial corporations (Fortune 500, 2006). Assume that you
The 10 most active stocks on the New York Stock Exchange on March 6, 2006, are shown here (The Wall Street Journal, March 7, 2006).AT&T Lucent Nortel Qwest Bell South Pfizer Texas Instruments Gen.
The following stocks make up the Dow Jones Industrial Average (Barron’s, March 23, 2009). 1.3M 11.Disney 21.McDonald’s 2.AT&T 12.DuPont 22.Merck 3.Alcoa 13.ExxonMobil
The Wall Street Journal provides the net asset value, the year-to-date percent return, and the three-year percent return for 555 mutual funds (The Wall Street Journal, April 25, 2003). Assume that a
A simple random sample of 5 months of sales data provided the following information:Month: 1 2345 Units Sold: 94 100 85 94 92a. Develop a point estimate of the population mean number of units sold
Many drugs used to treat cancer are expensive. BusinessWeek reported on the cost per treatment of Herceptin, a drug used to treat breast cancer (BusinessWeek, January 30, 2006).Typical treatment
A population has a mean of 200 and a standard deviation of 50.A simple random sample of size 100 will be taken and the sample mean will be used to estimate the population mean.a. What is the expected
Suppose a simple 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
Refer to the EAI sampling problem. Suppose a simple random sample of 60 managers is used.a. Sketch the sampling distribution of when simple random samples of size 60 are used.b. What happens to the
The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009):Critical Reading 502 Mathematics 515 Writing 494 Assume that
A simple random sample of size 100 is selected from a population with p .40.a. What is the expected value of ?b. What is the standard error of ?c. Show the sampling distribution of .d. What does the
A population proportion is .40. A simple random sample of size 200 will be taken and the sample proportion will be used to estimate the population proportion.a. What is the probability that the
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 500d. n
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 simple random sample of 800 households will be
Consider the following hypothesis test:A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.a. Compute the value of the test statistic.b. What is the p-value?c. At α
Consider the following hypothesis test:A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3.a. Compute the value of the test statistic.b. What is the p-value?c. At
Consider the following hypothesis test:A sample of 100 is used and the population standard deviation is 12.Compute the p-value and state your conclusion for each of the following sample results. Use
Consider the following hypothesis test:A sample of 60 is used and the population standard deviation is 8.Use the critical value approach to state your conclusion for each of the following sample
Consider the following hypothesis test:A sample of 75 is used and the population standard deviation is 10.Compute the p-value and state your conclusion for each of the following sample results. Use
Wall Street securities firms paid out record year-end bonuses of $125,500 per employee for 2005 (Fortune, February 6, 2006). Suppose we would like to take a sample of employees at the Jones & Ryan
Consider the following hypothesis test:A sample of 25 provided a sample mean 14 and a sample standard deviation s 4.32.a. Compute the value of the test statistic.b. Use the t distribution table
Consider the following hypothesis test:A sample of 48 provided a sample mean 17 and a sample standard deviation s 4.5.a. Compute the value of the test statistic.b. Use the t distribution table
Consider the following hypothesis test:A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α .01.a. 44 and s 5.2b. 43 and s
Consider the following hypothesis test:A sample of 65 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α .05.a. 103 and s 11.5b. 96.5 and
Consider the following hypothesis test:A sample of 400 provided a sample proportion .175.a. Compute the value of the test statistic.b. What is the p-value?c. At α .05, what is your conclusion?d.
Consider the following hypothesis test:A sample of 300 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use α .05.a. .68c. .70b. p¯
Consider the following hypothesis test.H0:Ha:μ 10μ 10 The sample size is 120 and the population standard deviation is assumed known with σ 5.Use α .05.a. If the population mean is 9, what
Consider the following hypothesis test.A sample of 200 items will be taken and the population standard deviation is σ 10.Use α .05. Compute the probability of making a Type II error if the
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed within 15 minutes or less. If more time is required, a premium rate is charged.
Young Adultmagazine states the following hypotheses about the mean age of its subscribers.a. What would it mean to make a Type II error in this situation?b. The population standard deviation is
Refer to exercise 48.Assume the firm selects a sample of 50 surveys and repeat parts (b)and (c). What observation can you make about how increasing the sample size affects the probability of making a
Consider the following hypothesis test.The sample size is 120 and the population standard deviation is 5.Use α .05. If the actual population mean is 9, the probability of a Type II error is .2912.
Consider the following hypothesis test.The population standard deviation is 10.Use α .05. How large a sample should be taken if the researcher is willing to accept a .05 probability of making a
Young Adult magazine states the following hypotheses about the mean age of its subscribers.If the manager conducting the test will permit a .15 probability of making a Type II error when the true
The following results come from two independent random samples taken of two populations.a. What is the point estimate of the difference between the two population means?b. Provide a 90% confidence
Consider the following hypothesis test.The following results are for two independent samples taken from the two populations.a. What is the value of the test statistic?b. What is the p-value?c. With
Consider the following hypothesis test.The following results are from independent samples taken from two populationsa. What is the value of the test statistic?b. What is the degrees of freedom for
Consider the following data for two independent random samples taken from two normal populations.Sample 1 10 7 13 7 9 8 Sample 2 87 8469a. Compute the two sample means.b. Compute the two sample
The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker’s parents. A research hypothesis was that students
Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the
Consider the following hypothesis test.The following data are from matched samples taken from two populations.a. Compute the difference value for each element.b. Compute .c. Compute the standard
The following data are from matched samples taken from two populations.a. Compute the difference value for each element.b. Compute .c. Compute the standard deviation sd.d. What is the point estimate
Bank of America’s Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses,
Consider the following results for independent samples taken from two populations.a. What is the point estimate of the difference between the two population proportions?b. Develop a 90% confidence
Consider the hypothesis test The following results are for independent samples taken from the two populations.a. What is the p-value?b. With α .05, what is your hypothesis testing conclusion?
Chicago O’Hare and Atlanta Hartsfield-Jackson are the two busiest airports in the United States. The congestion often leads to delayed flight arrivals as well as delayed flight departures. The
During the 2003 Super Bowl, Miller Lite Beer’s commercial referred to as “The Miller Lite Girls” ranked among the top three most effective advertisements aired during the Super Bowl (USA Today,

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