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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

=+Did the overall quality measure provided for these properties reflect these differences?
=+In Section 16.7 we saw data on commercial properties in a large U.S. city. One variable available for those properties is a “quality” ranking into one of 6 categories, with 1 as the “best”
=+6. As in Exercise 5, a process to make fishing strings produces spools with a desired mean length of 91.4 m (100 yds). The historical standard deviation is 1 cm (0.01 m). If samples of size 6 are
=+c) If the sample size were increased to 12, how would the answers to parts a and b change?
=+a) What is the center line for the R chart?
=+b) How long or short would the sample mean length would have to be to fall outside the 3s limit?
=+b) What is the standard deviation of the sample range?
=+a) What is the standard deviation of the sample mean?
=+5. A process to make fishing strings produces spools with a mean length of 91.4 m (100 yds). The historical standard deviation is 1 cm (0.01 m). If a sample size of 6 are taken and measured.
=+4. For the data in Exercise 1, suppose the historical standard deviation had been 0.1°C instead of 0.2°C. How would that change your answers to the questions in Exercise 3?Section 21.3
=+c) How large (or small) would the sample range have to be to fall outside the 3s limit?Section 21.5
=+g) Are any fourteen points in a row alternatively increasing and decreasing?h) Based on your answers to parts b–g, what do you conclude?
=+f) Are any six points in a row increasing (or decreasing)?
=+7. One of the ways in which the dental floss discussed in Exercise 5 can fail is if it snaps when pulled with a certain tension. Historically, only 2% of the tested floss snaps. Suppose boxes of
=+e) Are there eight points in a row on the same side of the mean?
=+d) Are four out of five consecutive points outside of 1s on either side?
=+c) Are two of three consecutive points outside of 2s on either side?
=+3. For the data in Exercise 1, instead of the specification limits,a) Use the historical standard deviation to set up 1, 2, and 3s limits and draw the control chart.b) Are any points outside the 3s
=+b) What might you recommend to the engineers given this value of Cp?Exercises Container #Temperature Loss 1°C2 Container #Temperature Loss 1°C2 1 3.89 7 4.22 2 3.71 8 4.02 3 4.14 9 4.48 4 4.12 10
=+2. A computer screen manufacturing process must produce screens of uniform size. In particular, for a new tablet, the screen should be 10.1 inches long. The engineers have set 10.16 and 10.04 as
=+b) What are the upper and lower 3s control limits?
=+a) Make a control chart of these data using the specification limits given.b) Does the process seem to be in control?c) What is the value of Cp for the process?d) Given this value of Cp, what
=+1. A producer of beverage containers wants to ensure that a liquid at 90°C will lose no more than 4°C after 30 minutes. Containers are selected at random and subjected to testing. Historical
=+Organize these possible factors into a fishbone (Ishikawa) diagram to help them design experiments using these factors.
=+c) How many packages in a box of 50 would have to fail for a process to be declared out of control using the 3s control limits?
=+Using X and R charts with the desired mean of 18.15 oz. and the desired standard deviation of 0.08 oz., does the process seem to be in control now? If not, when did the process seem to slip out of
=+parameter values, construct a runs chart for the following weights of recent batches and comment on whether the process is in control. 18.03 18.00 18.12 17.81 18.23 18.11 18.23 18.19 18.00 18.05
=+After the report in the example on page 776, the candy company makes some changes to the pouring process and thinks that the mean is now 18.15 oz. and the standard deviation is 0.08 oz. Using these
=+Perform a process capability analysis on the fudge shop and comment on your findings
=+ Do you see any potential problems with the analysis?
=+What conclusions about the additive and car types do you draw?
=+A plot of the residuals vs. predicted values showed:2.5 0–2.5–5.0 Residuals (mpg)12.5 25.0 37.5 50.0 Predicted Values (mpg)
=+Square F-ratio P-value Type 2 23175.4 11587.7 2712.2 60.0001 Additive 1 92.1568 92.1568 21.57 60.0001 Interaction 2 51.8976 25.9488 6.0736 0.0042 Error 54 230.711 4.27242 Total 59 23550.2
=+A two-way ANOVA with interaction model was run, and the following ANOVA table resulted.Source DF Sum of Squares Mean
=+48. Gas additives. An experiment to test a new gasoline additive, Gasplus, was performed on three different cars: a sports car, a minivan, and a hybrid. Each car was tested with both Gasplus and
=+c) If so, perform the hypothesis tests and state your conclusion. Be sure to state it in terms of head injury severity, seats, and vehicle types.
=+a) State the null hypotheses about the main effects (in words, not symbols).
=+A scatterplot of residuals vs. predicted values shows:0.6 0.3–0.3 0Residuals (severity index)2.8 2.9 3.0 3.1 Predicted Values (severity index)The ANOVA table follows:Source DF Sum of Squares Mean
=+Seat Effect (severity index)Driver Passenger Seat 2.7 2.4 3.0 3.3 Size Effect (severity index)Compact Light Medium Mini Pickup Van Size An interaction plot shows:2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5
=+47. Automotive safety. The National Highway Transportation Safety Administration runs crash tests in which stock automobiles are crashed into a wall at 35 mph with dummies in both the passenger
=+e) To check for significant differences between the shelf means, we can use a Bonferroni test, whose results are shown here. For each pair of shelves, the difference is shown along with its
=+d) Can we conclude that cereals on shelf 2 have a lower mean protein content than cereals on shelf 3? Can we conclude that cereals on shelf 2 have a lower mean protein content than cereals on shelf
=+c) What does the ANOVA table say about the null hypothesis? (Be sure to report this in terms of protein content and shelf placement.)
=+8. Rather than use the proportion of packages that contain defective floss, another quality control inspector simply counts the number of packages. If historically, only 1 package out of 50 is
=+46. Cereal shelf placement, part 2. We also have data on the protein content on the 77 cereals in Exercise 45. Does protein content vary by shelf? Here’s a boxplot and an ANOVA table.6 54 32
=+e) To check for significant differences between the shelf means, we can use a Bonferroni test, whose results are shown at the top of the next column. For each pair of shelves, the difference is
=+d) Can we conclude that cereals on shelf 2 have a different mean sugar content than cereals on shelf 3? Can we conclude that cereals on shelf 2 have a different mean sugar content than cereals on
=+c) What does the ANOVA table say about the null hypothesis? (Be sure to report this in terms of sugar content and shelf placement.)
=+b) What are the null and alternative hypotheses?
=+a) What kind of design or study is this?
=+45. Cereal shelf placement. Supermarkets often place similar types of cereal on the same supermarket shelf. The shelf placement for 77 cereals was recorded as well their sugar content. Does sugar
=+c) The P-value of this F-statistic turns out to be 0.00000949. What does this say about the null hypothesis of equal means?
=+42. Process improvements. One way to improve a process is to eliminate non–value-added activities (e.g., extra movements) and wasted effort (e.g., looking for materials). A consultant was hired
=+d) Based on the two-way ANOVA results, management concluded that shift has a significant impact on the length of the part and that consequently operator inexperience is the root cause of the part
=+Each scrubber was tested 5 times. For each run, the same material was produced, and the particulate emissions coming out of the scrubber were measured (in parts per billion). A partially complete
=+44. Smokestack scrubbers. Particulate matter is a serious form of air pollution often arising from industrial production. One way to reduce the pollution is to put a filter, or scrubber, at the
=+f) What is the average size of the error standard deviation?
=+e) What would you like to see to justify the conclusions of the F-test?
=+d) What assumptions have you made to answer part c?
=+c) The P-value of this F-statistic turns out to be 0.075.What does this say about the null hypothesis of equal means?
=+b) Form the F-statistic by dividing the two mean squares.
=+a) Calculate the mean square of the treatments and the mean square of the error.
=+43. Tax return forms. In order to improve the format of tax return forms, a government agency developed two new forms. To determine which, if any, are superior to the current form, 30 individuals
=+a) What is the standard deviation of the number of defective packages?
=+d) Based on the two-way ANOVA results, management concludes that neither the workspace design nor the storage/retrieval system impacts process flow time (and that the consultant wasn’t worth the
=+a) Is this an experiment or observational study? Explain.
=+c) How many treatments are involved?M20_SHAR8696_03_SE_C20.indd 765 14/07/14 7:37 AM 766 CHAPTER 20 Design and Analysis of Experiments and Observational Studies
=+that their relative inexperience may also be contributing to the variation. Three parts were randomly selected and measured from each treatment combination. The deviation from specified size was
=+41. Production problems. A manufacturing company that makes dental drills was experiencing problems with a specific part on the production line. Management suspected a machining problem that
=+c) How does the upper limit compare to the upper limit in Exercise 7, part c?Chapter Exercises
=+9. Super Glue®. Cyanoacrylates, the generic name for several compounds with strong adhesive properties, were invented during WWII during experiments to make a special extraclear plastic suitable
=+c) If so, perform the hypothesis tests and state your conclusions in terms of compressive strength, alkali content, and sand type.
=+samples were randomly selected from each treatment combination to be tested. The boxplots show the test results on compressive strength (in psi) for the three levels of alkali content and three
=+40. Concrete testing. A company that specializes in developing concrete for construction strives to continually improve the properties of its materials. To increase the compressive strength of one
=+Krazy® Glue. They are often sold in small quantities, typically 2-oz. tubes. The manufacturers want to ensure that the same quantity of glue goes into each tube so they monitored the process from
=+d) Is it appropriate to interpret the main effects in this case? Explain.
=+c) If so, perform the hypothesis tests and state your conclusions in terms of hourly wages, occupational type, and region.
=+b) Are the conditions for two-way ANOVA met?
=+39. Managers’ hourly wages. What affects marketing managers’ hourly wages? To find out, mean hourly wages were retrieved from the U.S. Bureau of Labor Statistics for two managerial
=+10. The R&A. The R&A requires that a golf ball used in a major league game have a diameter between 42 mm and 42.67 mm. Ben Hogan® is an official supplier of golf balls to the world golfing market.
=+c) Given the small P-value associated with the gender and that the mean annual bonus percent for females is 12.5%compared to 14.5% for males, HR concludes that gender discrimination exists. Do you
=+38. Company bonuses. After complaints about gender discrimination regarding bonus incentive pay, a large multinational firm collected data on bonuses awarded during the previous year (% of base
=+e) What does the interaction term test and what do you conclude about that?
=+d) What do you conclude about the average value of the DJIA in different months? Explain.
=+DJIA on different days of the week? Explain.
=+11. Pole vault. Pole vault technology has evolved considerably since the times of the ancient Greeks and even more recently as new materials have found their way into pole manufacturing. There are
=+c) What do you conclude about the average value of the
=+b) State the hypotheses.
=+37. Stock patterns. Some people believe that the stock market shows patterns according to the day of the week or the month of the year (“Sell in May and walk away”). We have the closing price
=+c) What are the factors?
=+a) Is this an experiment or an observational study? Explain.
=+less than 6.0 m wide and 6.15 m long. Should the manufacturers of landing pads treat these as specification or control limits? Explain.
=+36. Injection molding. To improve the quality of molded parts, companies often test different levels of parameter settings to find the best combinations. Injection molding machines typically have
=+e) State the hypotheses (in words, not symbols).
=+12. Milk production. Whether pasteurized or raw, both the European Economic Council (EEC) and the U.S. Food and Drug Administration (USFDA) require that milk sold to consumers contain no more than
=+d) How many treatments are involved?
=+c) How many factors are involved?
=+a) Is this an experiment or an observational study?Explain.
=+a transaction involving one of three products (book, camera, or insurance). These products represent varying degrees of risk. After completing the transaction, they rated how“trustworthy” the
=+35. E-trust. Online retailers want customers to trust their websites and want to alleviate any concerns potential customers may have about privacy and security. In a study investigating the

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