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mathematics
introduction to business statistics

Questions and Answers of Introduction to business statistics

The data in the table describe rug and carpeting shipments ($ billions) and the number of housing starts (millions) over a 6-year time period.a. Determine the least-squares regression line for
For 1998 and 1999, quarterly revenue and net income (millions of dollars) for Pacer Technology were as shown here.Determine the least-squares regression line and interpret its slope. Estimate net
The following data represent y = the number of passenger cars retired from service and x = the number of new passenger cars registered during the years 1991€“1995.a. Determine the
In regression analysis, what is a “residual”?
Testing the null hypothesis that the slope of the true regression line equals zero is equivalent to testing whether the true coefficient of correlation could be zero. Why?
Given the information in Exercise 15.12, determine and interpret the coefficients of correlation and determination for profit per partner versus the number of law partners.
The accompanying data show the U.S. population versus shipments of socks.a. Determine the least-squares regression line and calculate r.b. What proportion of the variability in sock shipments is
The following data show U.S. production of motor vehicles versus tons of domestic steel shipped for motor vehicle manufacture.a. Determine the least-squares regression line and calculate r.b. What
The ratings below are based on collision claim experience and theft frequency for 12 makes of small, two-door cars. Higher numbers reflect higher claims and more frequent thefts, respectively.a.
For a set of data, the total variation or sum of squares for y is SST =143.0, and the error sum of squares is SSE = 24.0. What proportion of the variation in y is explained by the regression equation?
The coefficient of correlation between variables y and x is 0.90. Calculate and interpret the value of the coefficient of determination.
Given the information in Exercise 15.12, determine and interpret the 90% confidence and prediction intervals associated with profit per partner when there are 150 law partners.
For the National Football League, ratings for the alltime leading passers were as shown below. Also shown for each quarterback is the percentage of passes that were interceptions, along with the
For a set of 8 data points, the sum of the squared differences between observed and estimated values of y is 34.72. Given this information, what is the standard error of estimate?
Is it possible for the standard error of estimate to be equal to zero? If so, under what circumstances?
For the highest-ranking law firms in terms of profit per partner, data file XR15012 lists the number of partners in each firm, along with the profit/partner for the reporting year. Given these data,
For the five top-grossing animated films of all time, the data in the table show gross ticket sales during the initial 2 weeks compared to total gross sales. Given these data, determine the
What is the least-squares criterion, and what does it have to do with obtaining a regression line for a given set of data?
In the linear regression equation ŷ = b0 + b1x why is the term at the left given ŷ as instead of simply y?
For the first 40 Super Bowl games, the winning margins are listed in file XR14061. At the 0.10 level of significance, can this sequence be considered as other than random? Identify and interpret the
For the first 40 Super Bowl games, the winner is listed in file XR14060 according to “1” (American Conference) or “2” (National Conference). At the 0.05 level of significance, can this
According to the U.S. Department of Transportation, the median age of automobiles and trucks on the road in the United States is about 8 years. The ages for a random sample of vehicles in the
In the runs test for randomness, what is a “run”?
The following salary figures have been reported for the mayor, police chief, and fire chief for a sample of U.S. cities. Assuming these are a random sample of major cities in the United States, and
A word-processing firm has narrowed down its choice of a printer to two major brands. Using a 20-page document that is typical of the firm’s work, a number of printers of each brand are timed while
A shop owner has collected random samples of sales receipts for credit purchases made with MasterCard and Visa. The amounts are listed in data file XR14025. At the 0.05 level, can we conclude that
Twelve family pets have been randomly placed into two groups. Group 1 receives the standard version of a flea powder, while group 2 receives a modified formula. Four days following treatment,
For the following random samples from two populations, use the 0.025 level of significance in testing H0 : m1 ≥ m2 versus H1 : m1 < m2. versus.Sample 1: 46.8 48.0 72.6 55.1 43.6
For the following random samples from two populations, use the 0.05 level of significance in testing H0 : m1 = m2 versus H1 : m1 ≠ m2.Sample 1: 40 34 53 28 41Sample 2: 29 31 52 29 20 31 26
What is the parametric counterpart to the Wilcoxon rank sum test? Compare the assumptions involved in using the respective tests.
Differentiate between the Wilcoxon signed rank test and the Wilcoxon rank sum test, and explain the circumstances under which each should be applied.
The median age for a male at the time of his divorce has been reported as 37.4 years. In a given region, a random sample of divorces showed the ages for the males as listed in data file XR14011.
What key feature distinguishes non parametric from parametric tests?
According to the Bureau of the Census, 39% of U.S. adults in the $20,001–$35,000 income group participated in adult education during the most recent reporting year. Data for this and other groups
The American Council of Life Insurance lists the following breakdown of ordinary life insurance policies purchased in the United States during the most recent reporting year. If a random sample of
It has been reported that 18.3% of all U.S. households were heated by electricity in 1980, compared to 26.5% in 1993 and 30.7% in 2001. At the 0.05 level, and assuming a sample size of 1000 U.S.
A Scenic America study of billboards found that 70% of the billboards in a sample observed in Baltimore advertised alcohol or tobacco products, compared to 50% in Detroit and 54% in St. Louis. Using
In carrying out a chi-square test for the independence of variables, what is the procedure for determining the number of degrees of freedom to be used in the test?
In conducting a chi-square test, why is it advisable that each expected frequency be at least 5.0? If the expected frequency in a cell happens to be less than 5.0, what should be done in order to
Approximately 13.3% of U.S. drivers are younger than age 25, with 39.2% in the 25–44 age group, and 47.5% in the 45-and-over category. For a random sample of 200 fatal accidents in her state, a
It has been reported that 10.3% of U.S. households do not own a vehicle, with 34.2% owning 1 vehicle, 38.4% owning 2 vehicles, and 17.1% owning 3 or more vehicles. The data for a random sample of 100
According to the Bureau of the Census, 19.0% of the U.S. population lives in the Northeast, 22.9% in the Midwest, 35.6% in the South, and 22.5% in the West. In a random sample of 200 recent calls to
Why can the chi-square statistic never be negative?
Sketch the approximate shape of the chi-square curve when df = 2 and when df = 100.
In what way are the chi-square and normal distributions related?
Is the chi-square distribution a continuous distribution or a discrete distribution? Explain.
Given the situation described in Exercise 12.85, which ANOVA procedure from this chapter would be appropriate for the analysis of the resulting data?
Three different faceplate designs have been selected for the radio intended for a new luxury automobile, and safety engineers would like to examine the extent to which their operation will be
The data in an experiment have been examined using ANOVA, and a confidence interval has been constructed for the mean associated with each level for a factor. Which ANOVA technique (one-way,
Since the t-tests of Chapter 11 and the ANOVA techniques of this chapter are both involved with the comparison of sample means, why can’t the techniques always be used interchangeably?
For Exercise 12.77, and using the levels of the “shopping bag carried” factor as the horizontal axis and “minutes” as the vertical axis, plot and connect the cell means for the cells
For Exercise 12.75, and using the levels of the assembly method factor as the horizontal axis and “units produced” as the vertical axis, plot and connect the cell means for the cells associated
In a two-way ANOVA experiment, factor A is operating on 4 levels, factor B is operating on 3 levels, and there are 3 replications per cell. How many treatments are there in this experiment? Explain.
In the two-way ANOVA, what is meant by the term replications?
What are main effects and interactive effects in the two-way ANOVA?
What assumptions are required in using the two way ANOVA?
What is the purpose of two-way analysis of variance?
Apply the dependent-samples t-test to the data in Exercise 12.53. Is the conclusion consistent with the one reached in that exercise? Explain.
In one-way ANOVA, we were able to determine the confidence interval for the population value of each treatment mean. Why is this not appropriate for the treatments being examined in the randomized
In the randomized block design, what benefit is gained from blocking?
What is the purpose of the randomized block design?
For the following summary table for a one-way ANOVA, fill in the missing items (indicated by asterisks), identify the null and alternative hypotheses, th en use the 0.025 level of significance in
Safety researchers, interested in determining whether the occupancy of a vehicle might be related to the speed at which the vehicle is driven, have observed the following speed (mph) measurements for
In terms of the assumptions required for using ANOVA, what is the special relevance of the value calculated for the error mean square, MSE?
Why is the F distribution applicable to ANOVA?
What assumptions are required in using the one-way ANOVA?What assumptions are required in using the one-way ANOVA?
What is the purpose of the one-way ANOVA?
The dotplots at the top of page 414 represent independent samples. Would you tend to reject the null hypothesis that µA = µB ? Explain.
For the experiment described in Exercise 12.8, identify the dependent and independent variables. Indicate whether each variable is quantitative or qualitative.
For the experiment described in Exercise 12.7, identify the dependent and independent variables. Indicate whether each variable is quantitative or qualitative.
For the experiment described in Exercise 12.6, identify the dependent and independent variables. Indicate whether each variable is quantitative or qualitative.
From each of four suppliers, a quality-control technician collects a random sample of 10 rivets, then measures the number of pounds each will withstand before it fails. Does this represent a designed
Twenty accounting students are randomly assigned to two different sections of an intermediate accounting class. Each section ends up consisting of 10 students. In one of the sections,
A university president collects data showing the number of absences over the past academic year for a random sample of 6 professors in the College of Engineering. She does the same for a random
Explain the basic role that between-sample variation and within-sample variation play in carrying out an analysis of variance.
What is necessary for an experiment to be “balanced”?
“A factor level is the same as a treatment.” Is this statement always true? If not, what conditions are necessary for it to be true?
What is meant by a designed experiment?
In a Maritz AmeriPoll survey, 16.6% of 500 males said they spend over $1000 per year on clothing. In a survey of 500 females, 11.8% said they spend over $1000 per year on clothing. In a two-tail test
According to the U.S. National Center for Education Statistics, 80% of college and university teachers use computers on the job, compared to 60% of teachers below the college level. Using a one-tail
Egbert Techster is very serious about winning this year’s All-American Soap Box Derby competition. Since there is no wind-tunnel time available at the aerospace firm where his father works, Egbert
For independent samples of customers of Internet providers A and B, the ages are as listed in file XR11073. Using the 0.05 level of significance in a nondirectional test, examine whether the
A Dun & Bradstreet survey of business owners found that 23% of female business owners had a business home page compared to 16% of male business owners. Assume that file XR11063 contains the
Medical researchers monitoring two groups of physicians over a 6-year period found that, of 3429 doctors who took aspirin daily, 148 died from a heart attack or stroke during this period. For 1710
A university president randomly selects 10 tenured faculty from the College of Arts and Sciences and 10 tenured faculty from the College of Business. Each faculty member is then asked to rate his or
Each of 20 consumers is provided with a package containing two different brands of instant coffee. A week later, they are asked to rate the taste of each coffee on a scale of 1 (poor taste) to 10
A pharmaceutical firm has checked the cholesterol levels for each of 30 male patients, then provided them with fish-oil capsules to take on a daily basis. The cholesterol levels are rechecked after a
In examining vendors’ service and technical support for desktop personal computers, PC Magazine reported an average of 16.5 minutes on hold when calling Gateway compared to 14.1 minutes for calls
Under what conditions is it appropriate to use the z-test as an approximation to the unequal-variances t-test when comparing two sample means?
It has been reported that males who are 55 or older spend an average of 43 minutes on-line, versus 38 minutes on-line daily for women in this age group. Assuming that file XR11030 contains the survey
It has been reported that the average visitor from Japan spent $1953 during a trip to the United States, while the average for a visitor from the United Kingdom was $1783. Assuming that file XR11029
Using the sample results in Exercise 11.14, construct and interpret the 90% confidence interval for the difference between the population means. Is the hypothesized difference (0.00) within the
The New York Stock Exchange has reported that the average number of stocks directly held by senior citizens is 4.3, compared to 2.0 stocks for “Baby Boomers.” Assume that data file XR11014
In Los Angeles, doctors carried out an experiment in which 105 sedentary people whose arteries were photographed were given a photograph of the inside of their arteries to carry around. Another 105
In a study by WebCriteria, it took an average of 2.1 minutes to locate information and buy products on the Delta Airlines website, compared to an average of 2.7 minutes on the British Airways site.
When comparing two sample means, the t-test should be used only when the sample sizes are less than 30.” Comment.
Based on the sample results in Exercise 10.109, construct and interpret the 95% confidence interval for the population proportion. Is the hypothesized proportion (0.27) within the interval? Given the
According to the U.S. Department of Justice, 27% of violent crimes involve the use of a weapon. We will assume that data file XR10109 contains a sample of the crime information for a given city, with
During 2000, 3.2% of all U.S. households were burglary victims. For a simple random sample of 300 households from a certain region, suppose that 18 households were victimized by burglary during that
The average U.S. household has $178,600 in life insurance. A local insurance agent would like to see how households in his city compare to the national average, and selects a simple random sample of

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