Question: The marketing department for an upscale retail
The marketing department for an upscale retail catalog company wants to determine if there are differences in the mean customer purchase amounts across the available purchase sources (Internet, phone, or mail-in). Accordingly, samples were taken for 20 random orders for each purchase source. The following output was compiled. Assume purchase amounts are normally distributed.
a. At the 5% significance level, can we conclude that the mean purchase amount is different across the three purchase sources?
b. If significant differences exist, use Fisher’s LSD method at the 5% significance level to determine which purchase sources have different mean purchase amounts.
Transcribed Image Text:
Internet Phone Mall-in Purchase Purchase Purchase X, = 214.05 n, = 20 X2 = 212.45 X3 = 182.40 n2= 20 n3 = 20 df MS F p-value Source of Variation 12715.23 2 6357.62 0.433 0.651 Between Groups 836704.70 57 14679.03 Within Groups Total 849419.93 59
> The home ownership rate in the U.S. was 67.4% in 2009. In order to determine if home ownership is linked with income, 2009 state-level data on the home ownership rate (Ownership in %) and median household income (Income in $) were collected. A portion of
> A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $72,000 with a standard deviation of $3,000. a. Using Chebyshev’s theorem, what percentage of the faculty earns at least $66,000 but
> When estimating a multiple linear regression model based on 30 observations, the following results were obtained. // a. Specify the hypotheses to determine whether x1 is linearly related to y. At the 5% significance level, are x1 and y linearly related
> A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. Estimate: Happiness = β0 + β1Age + ε. At the 1% significance level, is Age s
> The labor estimation group at Sturdy Electronics, a contract electronics manufacturer of printed circuit boards, wants to simplify the process it uses to quote production costs to potential customers. They have identified the primary drivers for producti
> The consumption function is one of the key relationships in economics, where consumption y depends on disposable income x. Consider the quarterly data for these seasonally adjusted variables, measured in billions of dollars. A portion of the data is show
> Healthy living has always been an important goal for any society. In an ad campaign for Walt Disney, former First Lady Michelle Obama shows parents and children that eating well and exercising can also be fun (USA Today, September 30, 2010). Consider a r
> Consider the monthly rent (Rent in $) of a home in Ann Arbor, Michigan, as a function of the number of bedrooms (Beds), the number of bathrooms (Baths), and square footage (Sqft). a. Estimate: Rent = β0 + β1Beds + β2Baths + β3Sqft + ε. b. Which of the e
> Consider the following regression results based on 40 observations. a. Specify the hypotheses to determine if the slope differs from minus one. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, does the s
> Quick2U, a delivery company, would like to standardize its delivery charge model for shipments (Charge in $) such that customers will better understand their delivery costs. Three explanatory variables are used: (1) distance (in miles), (2) shipment weig
> A simple linear regression, y = β0 + β1x + ε, is estimated with time series data. The resulting residuals e and the time variable t are shown in the accompanying table. a. Graph the residuals against time and look f
> A simple linear regression, y = β0 + β1x + ε, is estimated with cross-sectional data. The resulting residuals e along with the values of the explanatory variable x are shown in the accompanying table. a. Graph the r
> Consider a sample with 10 observations of −3, 8, 4, 2, −4, 15, 6, 0, −4, and 5. Use z-scores to determine if there are any outliers in the data; assume a bell-shaped distribution.
> Using 20 observations, the multiple regression model y = β0 + β1x1 + β2x2 + ε was estimated. A portion of the regression results is as follows: a. At the 5% significance level, are the explanatory variab
> The maintenance manager at a trucking company wants to build a regression model to forecast the time until the first engine overhaul (Time in years) based on four explanatory variables: (1) annual miles driven (Miles in 1,000s), (2) average load weight (
> Estimate: Price = β0 + β1Sqft + β2Beds + β2Baths + ε, where Price, Sqft, Beds, and Baths refer to home price, square footage, number of bedrooms, and number of bathrooms, respectively. Construct the 95% confidence interval for the expected price of a 2,5
> Estimate: Debt = β0 + β1Income + ε, where Debt (in $) is the average debt payments for a household in a particular city and Income (in $1,000s) is the city’s median income. a. Construct the 95% confidence interval for expected debt payments if income is
> GPA = β0 + β1GRE + ε, where GRE is a student’s score on the math portion of the Graduate Record Examination (GRE) score and GPA is the student’s grade point average in graduate school. a. Construct the 90% confidence interval for the expected GPA for an
> Estimate: Height = β0 + β1Fertilizer + ε, where Height is a tomato plant’s height (in inches) and Fertilizer is the fertilizer amount (in ounces). a. Calculate and interpret the 90% confidence interval for the mean height of a tomato plant that receives
> FILE Education. Estimate: Salary = β0 + β1Education + ε, where Salary is measured in $1,000s and Education refers to years of higher education. a. Construct the 90% confidence interval for the expected salary for an individual who completed 6 years of h
> Data are drawn from a bell-shaped distribution with a mean of 50 and a standard deviation of 12. There are 250 observations in the data set. Approximately how many observations are more than 74?
> An automotive workers union, in conjunction with top management, is negotiating a new hourly pay policy for union workers based on three variables: (1) job class, (2) years with the company, and (3) years as a union member at any company. The goal is to
> A multiple regression model is used to predict an NFL team’s winning record (Win in %). For the explanatory variables, the average rushing yards (Rush) and the average passing yards (Pass) are used to capture offense, and the average ya
> The manager of a local Costo store is in the process of making hiring decisions for selling mobile phone contracts. She believes that the sale of mobile phone contracts depends crucially on the number of hours clocked by male and female employees. She co
> A researcher interviews 50 employees of a large manufacturer and collects data on each worker’s hourly wage (Wage in $), years of higher education (EDUC), experience (EXPER), and age (AGE). A portion of the data is shown in the accompan
> Lisa Fisher is a business school professor who would like to analyze university factors that enhance innovation. She collects data on 143 universities in 2008 for a regression where the response variable is the number of startups (Startups), which is use
> A financial analyst believes that the best way to predict a firm’s returns is by using the firm’s price-to-earnings ratio (P⁄E) and its price-to-sales ratio (P⁄S) as explanatory vari
> Applications A real estate analyst estimates the following regression, relating a house price to its square footage (Sqft): In an attempt to improve the results, he adds two more explanatory variables: the number of bedrooms (Beds) and the number of ba
> Consider a portion of simple linear regression results, In an attempt to improve the results, two explanatory variables are added. The relevant regression results are the following: a. Formulate the hypotheses to determine whether x2 and x3 are joint
> Consider the multiple linear regression model, y = β0 + β1x1 + β2x2 + ε. Define the restricted and unrestricted models if the hypotheses are Hoi Bi + Bz = 1 and Ha: Bi + B2 # 1.
> A data set has a mean of 80 and a standard deviation of 5. a. Using Chebyshev’s theorem, what percentage of the observations fall between 70 and 90? b. Using Chebyshev’s theorem, what percentage of the observations fall between 65 and 95?
> Consider the multiple linear regression model, y = β0 + β1x1 + β2x2 + β3x3 + ε. You wish to test whether the slope coefficients β1 and β3 are statistically different from each other. Define the restricted and unrestricted models needed to conduct the tes
> On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. She believes that the performance on this math test and the number of hours studied per week on the course are the primary factors that p
> A realtor examines the factors that influence the price of a house in Arlington, Massachusetts. He collects data on recent house sales (Price) and notes each house’s square footage (Sqft) as well as its number of bedrooms (Beds) and num
> Caterpillar, Inc. manufactures and sells heavy construction equipment worldwide. The performance of Caterpillar’s stock is likely to be strongly influenced by the economy. For instance, during the subprime mortgage crisis, the value of
> The facility manager at a pharmaceutical company wants to build a regression model to forecast monthly electricity cost. Three main variables are thought to dictate electricity cost: (1) average outdoor temperature (Temp in °F), (2) working days per mont
> The maintenance manager at a trucking company wants to build a regression model to forecast the time until the first engine overhaul (Time in years) based on four explanatory variables: (1) annual miles driven (Miles in 1,000s), (2) average load weight (
> The cutting department at Best Cuts, a furniture manufacturer, is examining the effect of depth of cut and feed rate on the surface roughness of table legs used in a popular dining room table model. The accompanying table shows the surface roughness resu
> A production manager is investigating whether the operator training method (factor A) will affect the resulting output for a particular product. Three training methods were studied: a full-day workshop (most intensive), in-line training, and as-needed tr
> A management consultant wants to determine whether the age and gender of a restaurant’s wait staff influence the size of the tip the customer leaves. Three age brackets (factor A in columns: young, middle-age, older) and gender (factor
> An environmentalist wants to examine whether average fuel consumption (measured in miles per gallon) is affected by fuel type (factor A) and type of hybrid (factor B). A two-way ANOVA experiment with interaction is performed. The results are shown in the
> The accompanying table shows a portion of the annual return (in %) for the Fidelity Select Technology Fund and Fidelity Select Energy Fund from 2000 through 2016. Compare the sample means and the sample standard deviations of the two funds. Use a risk
> At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts. The judges use a scale of 1 to 10, where 10 is a perfect score. A statistician wants to examine the objectivity and consistency of the judges. Assume scores are n
> An automotive parts manufacturer is testing three potential halogen headlight designs, one of which ultimately will be promoted as providing best-in class nighttime vision. The distance at which a traffic sign can be read in otherwise total darkness is t
> The following output summarizes a portion of the results for a two-way ANOVA test without interaction where factor A (column) represents three income categories (low, medium, high), factor B (rows) consists of three different kinds of political parties (
> The accompanying table shows a portion of the results from conducting a two-way ANOVA test with no interaction in which five different production methods (factor A, columns) were evaluated in terms of labor cost per unit. Operator experience was used as
> Electrobat, a battery manufacturer, is investigating how storage temperature affects the performance of one of its popular deep-cell battery models used in recreational vehicles. Samples of 30 fully charged batteries were subjected to a light load under
> A data analyst for an online store wonders whether average customer visits to the store’s website vary by day of the week. He collects daily unique visits to the website for a 12-week period; a portion of the data is shown in the accomp
> An accounting professor wants to know if students perform the same on the departmental final exam irrespective of the accounting section they attend. She randomly selects the exam scores of 20 students from three sections. A portion of the output from co
> Before the Great Recession, job-creating cities in the Sunbelt, like Las Vegas, Phoenix, and Orlando saw their populations, income levels, and housing prices surge. Las Vegas, however, offered something that often eluded these other cities: upward mobili
> An economist wants to determine whether average price/earnings (P/E) ratios differ for firms in three industries. Independent samples of five firms in each industry show the following results: a. At the 5% significance level, determine whether average
> The following table shows the annual returns (in %) for the Fidelity Latin America Fund and the Fidelity Canada Fund from 2005 through 2009. a. Which fund had the higher average return? b. Which fund was riskier over this time period? c. Given a risk
> An employee of a small software company in Minneapolis bikes to work during the summer months. He can travel to work using one of three routes and wonders whether the average commute times (in minutes) differ between the three routes. He obtains the foll
> The marketing manager at Turfco, a lawn mower company, believes that monthly sales across all outlets (stores, online, etc.) are influenced by three key variables: (1) outdoor temperature (in °F), (2) advertising expenditures (in $1,000s), and
> Compressive strength of concrete is affected by several factors, including composition (sand, cement, etc.), mixer type (batch vs. continuous), and curing procedure. Accordingly, a concrete company is conducting an experiment to determine how mixing tech
> Finger dexterity, the ability to make precisely coordinated finger movements to grasp or assemble very small objects, is important in jewelry making. Thus, the manufacturing manager at Gemco, a manufacturer of high-quality watches, wants to develop a reg
> The Marketing Manager at Foodco, a large grocery store, wants to determine if store display location influences sales of a particular grocery item. He instructs employees to rotate the display location of that item every week and then tallies the weekly
> A government agency wants to determine whether the average salaries of four kinds of transportation operators differ. A random sample of five employees in each of the four categories yields the salary data (in $1,000s) given in the accompanying table.
> It is generally believed that a practical major such as business or engineering can really pay off for college graduates (CNNMoney.com, July 22, 2010). Other studies have shown that it is not just the major but also how students perform, as measured by t
> A human resource specialist wants to determine whether the average job satisfaction score (on a scale of 0 to 100) is the same for three different industries and three types of work experience. A randomized block experiment with interaction is performed.
> A consumer advocate examines whether the longevity of car batteries (measured in years) is affected by the brand name (factor A) and whether or not the car is kept in a garage (factor B). Interaction is suspected. The results are shown in the accompanyin
> The marketing group at Buy4Less, a local retail chain, is examining the effect of advertising at various times of day and on various local television channels. Based on 12-week cycles (4 time periods x 3 local channels), three observations (cycles) of we
> Fidelity_Select. The accompanying data file shows the annual return (in percent) for the Fidelity Select Technology Fund and the Fidelity Select Energy Fund from 2000 through 2016. Assume that the return data are bell-shaped. a. Use z-scores to determin
> Ask 20 of your friends whether they live in a dormitory, a rental unit, or other form of accommodation. Also find out their approximate monthly lodging expenses. Create a table that uses this information. What type of data do these numbers represent? Com
> The effects of detergent brand name (factor A) and the temperature of the water (factor B) on the brightness of washed fabrics are being studied. Four brand names and two temperature levels are used; six observations for each combination are examined. Th
> Applications The engineering department at a steel mill is studying the tensile strength of a particular grade of steel when fabricated at various pressures (Factor A) and temperatures (Factor B). The accompanying ANOVA table shows a portion of the resul
> A researcher conducts a two-way ANOVA test with interaction and provides the following ANOVA table. a. Find the missing values in the ANOVA table. b. At the 5% significance level, can you conclude that there is an interaction effect? c. At the 5% sign
> A researcher conducts a two-way ANOVA test with interaction and provides the following ANOVA table. a. At the 1% significance level, can you conclude that there is interaction between the two factors? b. Are you able to conduct tests based on the main
> A two-way analysis of variance experiment with interaction was conducted. Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each combination. The results include the following sum of squares term
> A two-way analysis of variance experiment with interaction was conducted. Factor A had four levels (columns), factor B had three levels (rows), and five observations were obtained for each combination. The results include the following sum of squares ter
> First National Bank employs three real estate appraisers whose job is to establish a property’s market value before the bank offers a mortgage to a prospective buyer. It is imperative that each appraiser values a property with no bias.
> The marketing manager at YumYum, a large deli chain, is testing the effectiveness of four potential advertising strategies. After a two-week trial period for each advertising strategy, sales were evaluated. However, since some store locations have higher
> Given a recent outbreak of illness caused by E. coli bacteria, the mayor in a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a restaurant’s cleanliness. In order to investigat
> Metalwork, a supplier of fabricated industrial parts, wants to determine if the average output rate for a particular component is the same across the three work shifts. However, since any of four machines can be used, the machine effect must be controlle
> A survey by AARP (Money, June 2007) reported that approximately 70% of people in the 50 to 64 age bracket have tried some type of alternative therapy (for instance, acupuncture or the use of nutrition supplements). Assume this survey was based on a sampl
> The following output summarizes a portion of the results for a two-way analysis of variance experiment with no interaction. Factor A consists of four different kinds of organic fertilizers, factor B consists of three different kinds of soil acidity level
> During a typical Professional Golf Association (PGA) tournament, the competing golfers play four rounds of golf, where the hole locations are changed for each round. Here are the scores for the top five finishers at the 2009 U.S. Open. The following st
> The following table summarizes a portion of the results for a two-way analysis of variance experiment with no interaction. a. Find the missing values in the ANOVA table. b. At the 5% significance level, can you conclude that the column means differ? c.
> The following table summarizes a portion of the results for a two-way analysis of variance experiment with no interaction. a. Find the missing values in the ANOVA table. b. At the 5% significance level, can you conclude that the column means differ?
> A two-way analysis of variance experiment with no interaction is conducted. Factor A has three levels (columns) and Factor B has five levels (rows). The results include the following sum of squares terms: a. Construct an ANOVA table. b. At the 5% signi
> A two-way analysis of variance experiment with no interaction is conducted. Factor A has four levels (columns) and Factor B has three levels (rows). The results include the following sum of squares terms: a. Construct an ANOVA table. b. At the 1% signi
> The following observations were obtained when conducting a two-way ANOVA experiment with no interaction a. Calculate SST, SSA, SSB, and SSE. b. Calculate MSA, MSB, and MSE. c. Construct an ANOVA table. e. At the 5% significance level, do the levels of
> The following observations were obtained when conducting a two-way ANOVA experiment with no interaction. a. Calculate SST, SSA, SSB, and SSE. b. Calculate MSA, MSB, and MSE. c. Construct an ANOVA table. e. At the 5% significance level, can you concl
> The accompanying table shows a portion of the number of customers that ate at a restaurant on weekend days over the past 52 weeks. a. Verify that the average number of customers that frequent the restaurant differs by weekend day at the 5% significance
> A production manager is examining whether work shift is related to employee absenteeism. The number of days absent over the past year was tallied for random samples of 25 workers on each shift. A portion of the data is shown in the accompanying table.
> On average, an American professional football game lasts about three hours, even though the ball is actually in play only 11 minutes (www.sportsgrid.com, January 14, 2014). Let the standard deviation be 0.4 hour. a. Use Chebyshev’s theorem to approximat
> Producers of a new grass seed called Pearl’s Premium claim that grass grown using its seed blend requires less maintenance as compared to other brands (The Boston Globe, July 4, 2009). For instance, grass grown using Pearlâ€&
> Elastotech, a plastics company, is trying to determine whether four successive daily batches of their Lexan polycarbonate have the same mean hardness value. Four daily samples of polycarbonate were taken, and the resulting hardness values were measured (
> Do energy costs vary dramatically depending on where you live in the United States? Annual energy costs are collected from 25 households in four regions in the United States. Sample means for each region and a portion of the ANOVA table is shown below.
> In an attempt to improve efficiency, Starbucks has implemented “lean” Japanese techniques at many of its 11,000 U.S. stores (The Wall Street Journal, August 4, 2009). By reducing the time baristas (employees) spend on
> The following output summarizes the results for a one-way analysis of variance experiment in which the treatments were three different hybrid cars and the variable measured was the miles per gallon (mpg) obtained while driving the same route. a. At th
> A one-way analysis of variance experiment produced the following ANOVA table. a. Use Fisher’s LSD method to determine which means differ at the 5% level of significance. b. Use Tukey’s HSD method to determine which m
> A one-way analysis of variance experiment produced the following ANOVA table. a. Conduct an ANOVA test at the 5% significance level to determine if some population means differ. b. Calculate 95% confidence interval estimates for μ1 &acir
> The following statistics are calculated by sampling from four normal populations whose variances are equal: a. Use Fisher’s LSD method to determine which population means differ at α = 0.01. b. Use Tukeyâ€
> The following statistics are computed by sampling from three normal populations whose variances are equal: a. Calculate 95% confidence intervals for μ1 − μ2, μ1 − Î&fra
> A human resource specialist wants to determine whether the average job satisfaction score (on a scale of 0 to 100) differs depending on a person’s field of employment. She collects scores from 30 employees in three different fields. A p
> An investment strategy has an expected return of 8% and a standard deviation of 6%. Assume investment returns are bell-shaped. a. How likely is it to earn a return between 2% and 14%? b. How likely is it to earn a return greater than 14%? c. How likel
> A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights
> At the 5% significance level, test whether the explanatory variables jointly influence sales. At the 1% significance level, test whether the unemployment rate is negatively related with sales. At the 1% significance level, test whether advertising expend
> According to a report by the government, new home construction fell to an 18-month low in October 2010 (CNNMoney.com, November 17, 2010). Housing starts, or the number of new homes being built, experienced an 11.7% drop in its seasonally adjusted annual
