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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+a) Create an X chart based on the calibration data statistics for these 24 hourly samples.
=+8. Analysts from the Internet company of Exercise 7 are now concerned that customers who come directly to their site (by typing their URL into a browser) might respond differently than those referred to the site from other sites(such as search engines). They decide to block according to
=+6. For the investment experiment of Exercise 4, identify how Control, Randomization, and Replication were used.Section 20.4
=+b) Create an R chart based on the calibration data statistics for these 24 hourly samples.
=+Wall Street Journal that listed stocks on the NYSE, and invested in each of the stocks hit by a dart, throwing a different set of darts for each of the three funds. At the end of six months the funds were compared.Section 20.3
=+c) Assuming that the process was in control during the calibration period, is the company’s process for making springs out of control?
=+An investment club decided to compare investment strategies. Starting with nine equal investment amounts, three invested in the “dogs of the Dow”—stocks in the Dow Industrial average that had been underperforming relative to the rest of the Dow average. The relative amounts to invest in
=+4. For the following experiment, identify the experimental units, the treatments, the response, and the random assignment.
=+3. For the following experiment, identify the experimental units, the treatments, the response, and the random assignment.A non-profit consumer protection department compared recipes for cakes. They baked cakes of different kinds(strawberry, chocolate, and banana). All other ingredients and
=+b) Does giving children a flu shot protect parents? Researchers questioned a random sample of families at the end of a flu season. They asked whether the children had been immunized, whether the parents had received flu shots, and who in the family had contracted the flu.Section 20.2
=+a) An airline was concerned that new security measures might discourage air travelers. A year after the new security restrictions were put into place, the airlines compared the miles traveled by their frequent fliers before and after the change.
=+21. Graphite production. A graphite manufacturer makes long rolls of flexible graphite to be used to seal components in combustion engines. The specifications state that the mean strength should be 21.2 ounces per square yard with a standard deviation of 0.29. Further specifications state that no
=+2. For the following observational studies, indicate whether they are prospective or retrospective studies.
=+b) An airline company solicited customers to join their“frequent flyer and loyalty program” and studied whether the new members did make use of the offers the company made to this group in comparison with non-members.
=+a) A restaurant reviewed a sample of comment cards from restaurant guests to estimate the annual income of families that dined in.
=+1. For the following observational studies, indicate whether they are prospective or retrospective.
=+22.2 ounces per square yard. If there is a defect in terms of the strength of the graphite rolls, the seal will not hold.After the roll is created, a beta scanner takes readings of the basis weight in ounces per square yard. The data is separated into 3 lanes with 20 scans in each lane. A sample
=+Suppose that you had run the randomized block design from Section 20.4 (see page 728). You would have had two levels of the (blocking) factor NE Corridor (NE or not) and the same four levels of Offer (Coupon, Card, Movie, and No Offer). The ANOVA shows a significant interaction effect between NE
=+What can you conclude?
=+7 Write a brief report. Can you conclude that the new formulation is safe and nutritious?
=+Are the assumptions and conditions for ANOVA satisfied?Coupon Card Movie No Offer–100 0 100 300 500 700 Offer Miles Traveled Offer vs. Miles Traveled 900
=+6 Both cats and dogs are to be tested. Should you block?Explain.
=+5 Would you use blinding? How? (Can or should you use double-blinding?)
=+4 How would you establish a control group?
=+What kind of design would this be? Diagram the experiment.
=+Explain how the four principles of experimental design are used in the Acela experiment described in the previous section (see page 724)
=+3 How would you implement control, randomization, and replication?
=+a) Using the given mean and standard deviation, create an X chart for these samples.
=+2 Identify the treatment and response.
=+What is the response variable?
=+ What are the subjects?
=+What are the factors and levels?
=+b) Using the given mean and standard deviation, create an R chart for these samples.
=+1 Suppose that, as a researcher for a pet food manufacturer, you are called on to plan a study seeking the cause of this problem. Specify how you might proceed. Would your study be prospective or retrospective?
=+ Can you conclude that Internet use is a factor in deciding to take the Acela?
=+c) Is the company’s process for making flexible graphite sheets out of control?
=+What kind of study is this?
=+d) Do all the rolls meet the specification limits?M21_SHAR8696_03_SE_C21.indd 802 14/07/14 7:36 AM Exercises 803
=+22. Graphite production, 10 lanes. The same graphite manufacturer from Exercise 21 uses an alternative process to make rolls. For this process the data are separated into 10 lanes—a sample consists of one roll from each lane. The results of 25 samples are shown in the table at the top of the
=+a) Using the same mean and standard deviation as given in Exercise 21, create an X chart for these samples.
=+b) Using the mean and standard deviation as in Exercise 21, create an R chart for these samples.
=+c) Is the company’s process for making flexible graphite sheets in control?
=+d) Are all of these rolls within the specification limits?
=+23. Defect monitoring. The following data are from a production process that makes 200 units each hour. The data were collected over a normal 12-hour shift one day. The data are shown in the table at the right.Using the first 10 hours as the calibration period,a) Calculate the center line of the
=+c) Calculate the lower control limit of the p chart.
=+d) Create a p chart for the samples from the second set of10 hours.
=+e) Is this process out of control?Hour No. of Defects Sample Size 1 11 200 2 9 200 3 17 200 4 19 200 5 15 200 6 15 200 7 18 200 8 21 200 9 18 200 10 6 200 11 27 200 12 14 200 13 7 200 14 18 200 15 19 200 16 18 200 17 17 200 18 15 200 19 7 200 20 16 200
=+Sample Lane 1 Lane 2 Lane 3 Lane 4 Lane 5 Lane 6 Lane 7 Lane 8 Lane 9 Lane 10 1 21.56 21.59 21.26 21.16 21.01 21.10 21.22 20.95 20.78 20.66 2 21.42 21.54 21.43 21.44 20.99 21.10 20.78 21.17 21.21 21.10 3 21.48 21.23 21.19 21.34 21.63 21.47 21.18 21.05 21.21 21.22 4 21.14 21.26 21.57 21.34 21.36
=+24. Defect monitoring, second product. The following data are from a production process that makes approximately 250 units each hour. The data were collected over a normal
=+12-hour shift one day. Historical data shows the proportion of defects to be 6.21%. Either use technology to accommodate the different sample sizes, or use 250 as an approximation for all of them.Hour No. of Defects Sample Size 1 13 241 2 18 265 3 17 256 4 14 249 5 20 221 6 19 276 7 12 244 8 15
=+b) Create a p chart for these samples.
=+c) Is this process out of control?
=+25. Computer chip manufacturing. MediaChip manufactures computer chips specifically for MP3 players. The process uses sophisticated lasers to imprint several hundred chips
=+sure to transform the se back to dollars if you are working with a transformed version of Cost.) Discuss how well your model predicts health care costs due to heart attack.
=+on a single silicon “wafer.” While the process is completely automated and set in a clean room environment, a batch of chips can contain imperfections that render the chips useless. This results in significant cost overruns.MediaChip would like to use a control chart to monitor their
=+6. Ultimately, how well can you predict Charges? Consider not just the R2, but also the se. (Be
=+5. Can you use DRG in your regression model as it is presented here, or should it be recoded in some way? Diagnosis raises similar questions. If our purpose is to predict costs based on demographic information, should these variables be predictors in our model?
=+4. How do men and women differ? Consider, for example, the distribution of Age for male and female patients. Should you introduce Sex as a variable in your model? How will you do that?
=+3. Some of these records may hold errors or otherwise be extraordinary. Make appropriate displays and set aside records that may not be reliable
=+2. Should LOS be re-expressed? Are there unusual features of the distribution that may deserve special attention?
=+1. Should Charges be re-expressed? Examine displays and find a suitable re-expression.
=+d) Why does the no trend model from Exercise 40 no longer work?
=+c) Would you use this model? Explain.
=+b) Is the trend term statistically significant?
=+a) Fit the linear model from Exercise 40 to this entire time period.
=+52. Hawaii tourism 2013, part 2. In Exercise 40, we fit a linear regression for the number of monthly international visitors to Hawaii (for the years 2002 through 2006) using Time and dummy variables for the months as predictors.The R2 value was 59.9% and a residual plot against Time would show
=+c) The impact of what two major events can you see in the plot of residuals against Time?
=+b) Would you use this model? Explain.
=+a) Fit the linear model from Exercise 39 to this entire time period.
=+51. Hawaii tourism 2013. In Exercise 39, we fit a linear regression for the number of monthly domestic visitors to Hawaii (for the years 2002 through 2006) using Time and dummy variables for the months as predictors. The R2 value was 96.6% and a residual plot against Time would show no
=+b) Is MediaChip’s manufacturing process in control?
=+d) Can you account for these changes? (Hint: Find the correlations among the Rate and lagged versions of the Rate.)
=+c) Add lag2 and lag3 components to the model. How do the coefficients change?
=+26. Supermarket Scanners. To speed up the checkout process, supermarkets use optical scanners. If the scanner fails to read the bar code of a product, the cashier manually enters the code into the register, which slows down the
=+b) Add a lag1 component to the model of (a). How does it change the coefficient of Year?
=+a) Fit a regression model with just Year as the predictor.
=+50. U.S. unemployment rate 2013, part 2. Using the data from Exercise 49 develop and compare the following models:
=+d) Comment on how these models do with these data.
=+c) Fit a single exponential smoothing model 1a = .72 to this series.
=+checkout process. A quality control team would like to determine whether a scanner is working properly. A sample of 500 scans is taken daily and the number of times the scanner is unable to read the bar code is determined. Out of 500 scans, management would like an average of no more than 7
=+b) Develop a 6-month and 12-month moving average model for this series.
=+a) What time series components do you observe in this series?
=+49. U.S. unemployment 2013. Following is the time series plot for the monthly U.S. Unemployment rate (%) from January 2003 to June 2013. These data have been seasonally adjusted (meaning that the seasonal component has already been removed).Year 2003 2005 2007 2009 2011 2013 Unemployment 5.59
=+c) For the model of Exercise 47 and the models of parts a andb, compute the MAPE. Which model did best? Given the plot in Exercise 47, explain why.d) Use these methods to forecast the crude oil price for April 2007. The April price was $60.48. Which forecast was closest? Does that mean it’s the
=+b) Find an exponential (multiplicative) model for this series.
=+a) Find a linear model for this series.
=+48. Oil prices, again. Return to the oil price data of Exercise
=+b) Obtain a forecast for March 2007.
=+47. Oil prices. A time series plot of monthly crude oil price($/barrel) from January 2001 to March 2007 is shown here.Month Year Jan 2001 Jan 2002 Jan 2003 Jan 2004 Jan 2005 Jan 2007 Jan 2006 Crude Price ($/Bar)10 20 30 40 50 60 70 M19_SHAR8696_03_SE_C19.indd 716 14/07/14 7:37 AM Exercises 717
=+d) Do you think this is an appropriate model for forecasting this time series?
=+b) Is the process out of control? Comment.M21_SHAR8696_03_SE_C21.indd 804 14/07/14 7:36 AM Exercises 805
=+c) Compare your forecast to the actual value (by computing APE).
=+b) Obtain a forecast for the week of May 28, 2007.
=+a) Fit an appropriate autoregressive model by testing for the significance of each autoregressive term.
=+42, develop and compare the following models.
=+27. Patient complaints. The following data were collected from the number of patient complaints from a small medical service facility over a two-week period. The past year the average number of complaints was 4.57. The management team would like to use that as a baseline for monitoring.Day 1 2
=+46. Monthly gas prices, part 3. Using the data from Exercise
=+c) Which model fits better?
=+b) Fit an exponential trend (multiplicative) model with dummy variables to these data.
=+a) Fit a linear trend model with dummy variables for the seasonal effect to the e-commerce data in Exercise 44.
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