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Business Statistics Communicating With Numbers 2nd Edition Sanjiv Jaggia, Alison Kelly - Solutions

Consider the following competing hypotheses and relevant summary statistics:H0: ????21 ∕ ????22 = 1HA: ????21 ∕ ????22 ≠ 1Sample 1: X̅1 = 48.5, s21 = 18.7, and n1 = 10Sample 2: X̅2 = 50.2, s22 =12.9, and n2 = 8Assume that the two populations are normally
Consider the following competing hypotheses and relevant summary statistics:H0: ????21 ∕ ????22 ≤ 1HA: ????21 ∕ ????22 > 1Sample 1: s21= 935 and n1 = 14Sample 2: s22 = 812 and n2 = 11Use the critical value approach to conduct this hypothesis test at the 5% significance
Consider the following competing hypotheses and relevant summary statistics:H0: ????21 ∕ ????22 ≥ 1HA: ????12 ∕ ????22 < 1Sample 1: s21= 1,315 and n1 = 17Sample 2: s22 = 1,523 and n2 = 19Conduct this hypothesis test at the 5% significance level. State your
A firm has just developed a new cost-reducing technology for producing a certain replacement part for automobiles. Since a replacement part must be produced within close specifications in order for it to be acceptable to customers, the new technology's specifications must not deviate drastically
Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the players are not equally consistent in their games. Over a 10-game period, the scores of these two
The following table shows the annual returns (in percent) for Fidelity's Electronic and Utilities funds.Using the critical value approach, test if the population variances differ at the 5% significance level. State your assumptions.
Nike's total revenues (in millions of $) for the Asian and Latin American regions for the years 2005 through 2009 are as follows:a. Specify the competing hypothesis in order to test whether the variance in revenues is greater in Asia than in Latin America.b. Calculate the value of the test
The quality manager at a battery manufacturing company wants to determine if lithium-ion batteries have less variability in discharge time than nickel-cadmium batteries. Using products with similar power draws, he has measured the time until discharge (in hours) for random samples of 16 lithium-ion
A marketing analyst is studying the variability in customer purchase amounts between shopping mall stores and "big box" discount stores. She suspects the variability is different between those stores due to the nature of the customers involved. To investigate this issue in detail, she compiled two
A portion of the monthly stock prices (rounded to the nearest dollar) for Starbucks Corp. and Panera Bread Co. from 2010 to 2013 are reported in the following table.a. State the null and the alternative hypotheses in order to determine if the variance of price differs for the two firms. b. What
A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A packaging company is trying out a new packaging material that might reduce the variation of
The data accompanying this exercise include monthly rents for a two-bedroom apartment in two campus towns: Ann Arbor, Michigan, and Davis, California. Davis, California is known to have higher rents than Ann Arbor, Michigan; however, it is not clear if it also has higher variability in rents. At a
A replacement part for a machine must be produced within close specifications in order for it to be acceptable to customers. A production process is considered to be working properly as long as the variance in the lengths of the parts does not exceed 0.05 squared-units. Suppose the sample variance
A random sample of 25 observations is used to estimate the population variance. The sample mean and sample standard deviation are calculated as 52.5 and 3.8, respectively. Assume that the population is normally distributed. a. Construct the 90% interval estimate for the population variance. b.
A consumer advocacy group is concerned about the variability in the cost of a generic drug. There is cause for concern if the variance of the cost exceeds 5 ($)2. The group surveys seven local pharmacies and obtains the following prices (in $) for a particular generic drug: 32, 36, 38, 32, 40, 31,
A financial analyst maintains that the risk, measured by the variance, of investing in emerging markets is more than 280(%)2. Data on 20 stocks from emerging markets revealed the following sample results: = 12.1(%) and s2 = 361(%)2. Assume that the returns are normally distributed. a. Specify the
Fizzco, a beverage manufacturing company, is interested in determining whether the standard deviation of their dispensing process has changed from a required level of 5 milliliters. They have taken a random sample of 12 bottles and have measured the amount of beverage dispensed into each bottle (in
For staffing purposes, a retail store manager would like to standardize the number of checkout lanes to keep open on a particular shift. She believes that if the standard deviation of the hourly customer arrival rates is 8 customers or less, then a fixed number of checkout lanes can be staffed
The following table presents a portion of the annual returns for Fidelity's Select Automotive Fund (in percent). This mutual fund invests primarily in companies engaged in the manufacturing, the marketing, or the sales of automobiles, trucks, specialty vehicles, parts, tires, and related
John Daum and Chris Yin are star swimmers at a local college. They are preparing to compete at the NCAA Division II national championship meet, where they both have a good shot at earning a medal in the men's 100-meter freestyle event. The coach feels that Chris is not as consistent as John, even
Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers' tastes and current fads. Consider the following growth rates (in percent) for two companies in this industry, Hasbro and Mattel.a. State the null and the alternative hypotheses in
At Burger Joint, consistency in product and service is the new motto. Accordingly, management has invested in an automated French-fry dispenser to replace the manual dispensing method. The goal is to standardize the number of fries provided. The accompanying table shows the number of fries
An automotive parts distributor wants to standardize its safety stock level for two parts, A and B. ("Safety stock" is the excess inventory carried above the expected demand level to provide protection against demand variability.) Consequently, the distributor has randomly sampled daily demand for
Barbara Dwyer, the manager at Lux Hotel, makes every effort to ensure that customers attempting to make phone reservations do not have to wait too long to speak with a reservation specialist. Since the hotel accepts phone reservations 24 hours a day, Barbara is especially interested in maintaining
The following values are drawn from a normal population. 20 29 32 27 34 25 30 31 a. Calculate the point estimates for the population variance and the population standard deviation. b. Construct the 95% confidence interval for the population variance and the population standard deviation
Adidas revenues (in millions of ‚¬) in Asia and Latin America for the years 2005 through 2009 are shown in the accompanying table. Assume revenues are normally distributed.a. Specify the competing hypothesis in order to test whether the variance in revenues is greater in Asia than in Latin
In order to conduct a hypothesis test for the population variance, you compute s2 = 75 from a sample of 21 observations drawn from a normally distributed population. Use the critical value approach to conduct the following tests at α = 0.10.a. H0: ????2 ≤ 50; HA: ????2 > 50b.
Consider the following hypotheses:H0: ????2 = 200HA: ????2 ≠ 200Approximate the p-value based on the following sample information, where the sample is drawn from a normally distributed population.a. s2 = 300; n = 25b. s2 = 100; n = 25c. Which of the above sample information enables us
You would like to test the claim that the variance of a normally distributed population is more than 2 squared units. You draw a random sample of 10 observations as 2, 4, 1, 3, 2, 5, 2, 6, 1, 4. At α = 0.10, test the claim using (a) The p-value approach and (b) The critical value approach.
A research analyst is examining a stock for possible inclusion in his client's portfolio. Over a 10-year period, the sample mean and the sample standard deviation of annual returns on the stock were 20% and 15%, respectively. The client wants to know if the risk, as measured by the standard
Due to environmental concerns and the never-ending volatility of gas prices, drivers are becoming more concerned with their cars' as oline consumption.Cameron White, a research analyst at a nonprofit organization, shares these concerns and wonders whether his car's gas consumption is as efficient
Nicholas Grammas is an investment analyst examining the performance of two mutual funds with Janus Capital Group: The Janus Balanced Fund and the Janus Overseas Fund.â€¢ The Janus Balanced Fund: This "core" fund consists of stocks and bonds and its goal is diversification. It has historically
For decades, people have believed that boys are innately more capable than girls in math. In other words, due to the intrinsic differences in brains, boys are better suited for doing math than girls. Recent research challenges this stereotype, arguing that gender differences in math performance
The quality department at an electronics company has noted that, historically, 92% of the units of a specific product pass a test operation, 6% fail the test but are able to be repaired, and 2% fail the test and need to be scrapped. Due to recent process improvements, the quality department would
An agricultural grain company processes and packages various grains purchased from farmers. A high-volume conveyor line contains four chutes at the end, each of which is designed to receive and dispense equal proportions of grain into bags. Each bag is then stamped with a date code and the number
A marketing agency would like to determine if there is a relationship between union membership and type of vehicle owned (domestic or foreign brand). The goal is to develop targeted advertising campaigns for particular vehicle brands likely to appeal to specific groups of customers. A survey of 500
(Use Excel) The quality manager believes there may be a relationship between the experience level of an inspector and whether a product passes or fails inspection. Inspection records were reviewed for 630 units of a particular product, and the number of units which passed and failed inspection was
(Use Excel) According to a 2008 survey by the Pew Research Center, people in China are highly satisfied with their roaring economy and the direction of their nation (USA Today, July 22, 2008). Eighty-six percent of those who were surveyed expressed positive views of the way China is progressing and
Consider the following sample data with mean and standard deviation of 20.5 and 5.4, respectively.Class .............................. FrequencyLess than 10 ............................. 2510 up to 20 .............................. 9520 up to 30 .............................. 6530 or more
The following frequency distribution has a sample mean of -3.5 and a sample standard deviation of 9.7.Class ............................ FrequencyLess than -10 ....................... 70-10 up to 0 .......................... 400 up to 10 ............................ 8010 or more
You are given the following summary statistics from a sample of 50 observations:Mean ................................ 77.25Standard Deviation ............... 11.36Skewness ........................... 1.12Kurtosis ............................. 1.63a. Using the Jarque-Bera test, specify the null and
An economics professor states on her syllabus that final grades will be distributed using the normal distribution. The final averages of 300 students are calculated, and she groups the data into a frequency distribution as shown in the accompanying table. The mean and the standard deviation of the
Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution. The sample mean and the sample standard deviation are 9% and 3.6%, respectively.Vacancy Rate (in percent) .................. FrequencyLess than 6
A multinomial experiment produced the following results:Can we conclude at the 1% significance level that not all population proportions are equal to 0.20?
The quality department at an electronics component manufacturer must ensure that their components will operate at prespecified levels. The accompanying table shows a frequency distribution with measured resistance values (in ohms) for a sample of 520 resistors. The sample mean and the sample
Fabco, a precision machining shop, uses statistical process control (SPC) techniques to ensure quality and consistency of their steel shafts. The control limits used in their SPC charts are based on the assumption that shaft diameters are normally distributed. To verify this assumption, a quality
Total 2005 CEO compensation for the largest U.S. companies by revenue is reported in the following frequency distribution, along with some summary statistics. Total compensation includes salary, bonuses, stock and incentives, the potential value of stock options, and gains from stock options
The following frequency distribution shows the distribution of monthly returns for Starbucks Corp. for the years 2003 through 2007.Class (in percent) ...................... FrequencyLess than -5 ................................ 14-5 up to 0 .................................... 90 up to 5
The data that accompanies this exercise show weekly stock prices for Home Depot.a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not Home Depot's weekly stock prices follow the normal distribution.b. Calculate the value of the Jarque-Bera test
The data that accompanies this exercise show miles per gallon (MPG) for a sample of 25 cars.a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not MPG follow the normal distribution.b. Calculate the value of the Jarque-Bera test statistic. Use Excel to
The following frequency distribution shows the monthly stock returns for Home Depot for the years 2003 through 2007.Class (in percent) .................... Observed FrequencyLess than -5 .................................... 13-5 up to 0 ....................................... 160 up to 5
The data that accompany this exercise show various variables, including price and square footage, for 36 single family homes in Arlington, Massachusetts, sold in the first quarter of 2009.a. Use the Jarque-Bera test to test if house prices are not normally distributed at α = 0.05.b. Use the
An automotive parts company has been besieged with poor publicity over the past few years due to several highly publicized product recalls which have tarnished its public image. This has prompted a series of quality improvement initiatives. Currently, the marketing manager would like to determine
Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose "green" status indicates that an assembly line is operating normally, "yellow" indicates it is down waiting on personnel for set up or repair, "blue"
The operations manager at Electro Tech, an electronics manufacturing company, believes that workers on particular shifts may be more likely to phone in "sick" than those on other shifts. To test this belief, she has compiled the following table containing frequencies based on work shift and days
The human resources department would like to consolidate the current set of retirement plan options offered to specific employee pay groups into a single plan for all pay groups (salaried, hourly, or piecework). A sample of 585 employees of various pay groups were asked which of three potential
A software company develops and markets a popular business simulation/modeling program. A random number generator contained in the program provides random values from various probability distributions. The software design group would like to validate that the program is properly generating random
Reorder point decisions for a particular part at an automotive parts distributor are based on the assumption that weekly demand is normally distributed. ("Reorder point" is the inventory level at which a replenishment order is placed; it should be high enough to cover demand during the order
Matthew Jordon is a research analyst for a large investment firm. He is preparing a report on the stock performance of Nike, Inc. One aspect of his report will contain inferences concerning monthly stock returns. Before making valid inferences, Matthew first wants to determine whether the return
Wenton Power sports produces dune buggies. They have three assembly lines, "Razor," "Blazer," and "Tracer," named after the particular dune buggy models produced on those lines. Each assembly line was originally designed using the same target production rate. However, over the years, various
In the carbonated beverage industry, dispensing pressure can be an important factor in achieving accurate fill volumes. Too little pressure can slow down the dispensing process. Too much pressure can create excess "fizz" and, thus, inaccurate fill volumes. Accordingly, a leading beverage
The following statistics are computed by sampling from three normal populations whose variances are equal:x1 = 25.3, n1 = 8; x2 = 31.5, n2 = 10; x3 = 32.3, n3 = 6;MSE = 27.2a. Calculate 95% confidence intervals for μ1 − μ2, μ1 − μ3, and μ2 − μ3 using Fisher's LSD approach.b. Repeat the
The following statistics are calculated by sampling from four normal populations whose variances are equal:x1 = 149, n1 = 10; x2 = 154, n2 = 10; x3 = 143, n3 = 10;x4 = 139, n4 = 10; MSE = 51.3a. Use Fisher's LSD method to determine which population means differ at α = 0.01.b. Use Tukey's HSD
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 Î¼1 âˆ’ Î¼2, Î¼1 âˆ’ Î¼3, and Î¼2 âˆ’ Î¼3 with
The following Excel 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.Hybrid 1: x1 = 38, n1 = 20Hybrid 2: x2 = 48, n2 =
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 bending, reaching, and walking, they will have more time to interact with
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 (using the Rockwell R scale). The following
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 Pearl's Premium needs mowing only once a month. Suppose an independent tester
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.First ShiftSecond ShiftThird
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.d. At a 1% significance level, can you conclude that the column means differ?e. At a 1% significance
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.d. At the 5% significance level, do the levels of Factor B differ?e. At the 5% significance level,
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: SST = 1,630.7 SSB = 532.3 SSE = 374.5 a. Construct an ANOVA table. b. At the 1% significance
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: SST = 311.7 SSA = 201.6 SSE = 69.3 a. Construct an ANOVA table. b. At the 5% significance
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. At the 5% significance level, can you conclude
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. At the 5% significance level, can you conclude
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 statistics were computed: SST = 272.95 SSB = 93.2
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 levels, and the variable measured is the height
Metalworks, 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 controlled for within the sample. The accompanying
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 investigate this possibility, the mayor has five restaurant inspectors
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 determined. However, since some store locations have higher customer traffic than other locations, the
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. Suppose First National Bank wishes to check the consistency of
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 terms:SST = 2500 SSA = 1200 SSB = 1000 SSE =
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 terms: SST = 1558 SSA = 1008 SSB = 400 SSAB =
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 effects? If yes, conduct these tests at the 1%
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% significance level, can you conclude that the column
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 results from conducting a two-way ANOVA test with
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, and six observations for each combination are examined. The following ANOVA table is produced.a.
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 weekly sales data have been obtained for each
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 accompanying table.……...…………………Brand
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. The results are shown in the accompanying
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 their GPA, that influences their salaries.
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 sales at each location over a 24-week period
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 technique affects the resulting compressive
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
The accompanying table shows a portion of job satisfaction scores (on a scale of 0 to 100) categorized by a person's field of expertise.Field 1Field 2Field
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 each of four different storage temperature
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 (dependent variable). Operator experience was used as a blocking factor
The following Excel output for Î± = 0.05 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 (Democrat,
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 the variable of interest. Since older drivers
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. She performs a two-way ANOVA analysis without interaction using

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