Solved: Restaurant Service Times Recall that DS 6.1.4

Restaurant Service Times (a) Construct the empirical cumulative distribution function for the data set of restaurant service times given in DS 6.1.4. (b) Draw 95% condence bands around the empirical cumulative distribution function. (c) Is it plausible that the service times are normally distributed with a mean of 70 seconds and a standard deviation of 20 seconds? (d) Is it plausible that the service times are exponentially distributed with a mean of 70 seconds? (e) Consider the null hypothesis that the median service time is no longer than 65 seconds. What statistic is used by the sign test procedure to test this null hypothesis? What is the p-value? (f) Test the null hypothesis in part (e) using the signed rank test. (g) Use the sign test and the signed rank test to obtain 95%condenceintervalsonthemedianservicetime.

Paving Slab Weights (a) Construct the empirical cumulative distribution function for the data set of paving slab weights given in DS 6.1.7. (b) Draw 95% condence bands around the empirical cumulative distribution function. (c) Is it plausible that the paving slab weights are normally distributed with a mean of 1.1 kg and a standard deviation of 0.05 kg? How about with a mean of 1.0 kg and a standard deviation of 0.05 kg? (d) Consider the null hypothesis that the median paving slab weight is 1.1 kg. What statistic is used by the sign test procedure to test this null hypothesis? What is the p-value? (e) Test the null hypothesis in part (d) using the signed rank test and the t-test. Compare your answers. (f) Use the sign test, the signed rank test, and the t-test to obtain 95% condence intervals for the median (or mean) paving slab weight. What assumptions are required by these three test procedures? Do the assumptions seem appropriate? How would you summarize your results?

Spray Painting Procedure Construct the empirical cumulative distribution function for the data set of paint thicknesses given in DS 6.1.8. Draw 95% condence bands around the empirical cumulative distribution function. Analyze the median (or mean) paint thickness using the sign test, the signed rank test, and the t-test. Pay particular attention to whether the median paint thickness is 0.2 mm. Which analysis method do you prefer? Summarize your conclusions.

Plastic Panel Bending Capabilities Construct the empirical cumulative distribution function for the data set of deformity angles given in DS 6.1.9.Draw 95% condence bands around the empirical cumulative distribution function. Analyze the median (or mean) deformity angle using the sign test, the signed rank test, and the t-test. Do you think that the assumptions behind these test procedures are valid? What evidence is there that the plastic can bend less than 9.5 on average before deforming?

Suppose that the data set in DS 15.1.1 consists of values that can be taken to be independent observations from a particular distribution. Consider testing whether the median of the distribution is equal to 18.0 against a two-sided alternative. (a) What is the value of the test statistic used by the sign test? (b) Write down an expression for the exact p-value using the sign test. (c) Use the normal approximation to calculate the p-value using the sign test. (d) What is the value of the test statistic used by the signed rank test? (e) Use the normal approximation to calculate the p-value using the signed rank test.

Repeat Problem 15.1.5 using the data set in DS 15.1.2 and for the null hypothesis that the median of the distribution is equal to 40 against a two-sided alternative hypothesis.

Production Line Assembly Methods Use the sign test and the signed rank test to analyze the paired data set of assembly times given in DS 9.2.1. Why might it be expected that the signed rank test is a better test procedure than the sign test for this paired data set? Do you nd any evidence of a difference between the two assembly methods?

Red Blood Cell Adherence to Endothelial Cells Use the sign test and the signed rank test to analyze the paired data set of adherent red blood cells given in DS 9.2.2. Do you nd any evidence of a difference between the two stimulation conditions?

Calculus Teaching Methods Use the sign test and the signed rank test to analyze the paireddatasetofcalculusscoresgiveninDS9.2.4.Doyou ndanyevidenceofadifferencebetweenthetwoteaching methods? How much better is the new teaching method?

Radioactive Carbon Dating Use the sign test and the signed rank test to analyze the paired data set given in DS 9.2.5 concerning the radioactive carbon dating methods. Do you nd any evidence of a difference between the two dating methods?

Golf Ball Design Use the sign test and the signed rank test to analyze the paireddatasetofgolfshotsgiveninDS9.2.6.Doyound any evidence of a difference between the two ball types?

Carbon Footprints Analyze the data in DS 6.7.15, which contain estimates of the pounds of carbon dioxide released when making several types of car.

Data Warehouse Design Powerconsumptionrepresentsalargeproportionofadata centers costs. Use nonparametric methods to analyze the data in DS 6.7.16, which shows monthly electricty costs as a percentage of the data centers total costs.

Customer Churn Customer churn is a term used for the attrition of a companys customers. DS 6.7.17 contains information from an Internet service provider on the length of days that its customers were signed up before switching to another provider. Use the techniques described in this section to analyze this data.

Mining Mill Operations DS 6.7.18 contains daily data for the mill operations of a mining company over a period of a month. Each day, the company keeps track of the carbon concentration in the waste material. Use the techniques described in this section to analyze this data.

Restaurant Service Times Recall that DS 6.1.4 shows the service times of customers at a fast-food restaurant who were served between 2:00 and 3:00 on a Saturday afternoon, and that DS 9.3.5 shows the service times of customers at the fast-food restaurant who were served between 9:00 and 10:00 in the morning on the same day. (a) Make a plot of the empirical cumulative distribution functions of these two data sets. (b) What does a visual comparison of the two empirical cumulative distribution functions suggest about the differencebetweenthetwoservicetimedistributions? (c) Use the Kolmogorov-Smirnov test to assess the evidence that the two distribution functions are different.

Paving Slab Weights Recall that DS 6.1.7 shows the weights of a sample of paving slabs from manufacturer A and that DS 9.3.1 shows the weights of a sample of paving slabs from manufacturer B. (a) Make a plot of the empirical cumulative distribution functions of these two data sets. (b) What does a visual comparison of the two empirical cumulative distribution functions suggest about the difference between the distributions of the paving slabs weights for the two manufacturers? (c) Use the Kolmogorov-Smirnov test to assess the evidencethatthetwodistributionfunctionsaredifferent.

Heel-Strike Force on a Treadmill DS 9.3.3 contains observations of heel-strike force for a runner on a treadmill with and without a damped feature activated. Use plots of the empirical cumulative distribution functions and the Kolmogorov-Smirnov test to investigate whether the damped feature is effective in reducing the heel-strike force.

Use the rank sum test procedure to analyze the two samples in DS 15.2.1. (a) Combine the two samples and rank the observations. (b) What is SA? (c) What is UA? (d) Is the value of UA consistent with the observations from population A being larger or smaller than the observations from population B? (e) Use a computer package to nd a two-sided p-value for the null hypothesis that the two distribution functions are identical. Is the difference between the two distribution functions suggested in part (d) statistically signicant?

Repeat Problem 15.2.4 using the data set in DS 15.2.2.

Use the rank sum test to analyze the data set in Figure 9.20 concerning Example 51 on acrophobia treatments. Let population A be with the standard treatment and population B be with the new treatment. (a) Combine the two samples and rank the observations. (b) What is SA? (c) What is UA? (d) Is the value of UA consistent with the new treatment being better than the standard treatment? (e) Use a computer package to nd a one-sided p-value for the null hypothesis H0 : A B versus the alternative hypothesis HA : A < B. (f) Are your conclusions from this analysis consistent with the analysis presented in Section 9.3.4 using the two-sample t-test?

Spray Painting Procedure Recall that DS 6.1.8 contains a sample of paint thicknesses from production line A and that DS 9.3.2 contains a sample of paint thicknesses from production line B. (a) Make a plot of the empirical cumulative distribution functions of these two data sets. (b) What does a visual comparison of the two empirical cumulative distribution functions suggest about the difference between the distributions of the paint thicknesses from the two production lines? (c) Use the Kolmogorov-Smirnov test to assess the evidencethatthetwodistributionfunctionsaredifferent. (d) Use the rank sum test to assess the evidence that the two distribution functions are different. Obtain a 95% condence interval for the difference between the median paint thicknesses for the two production lines. On what assumption is the rank sum test based? Do you think that it is a reasonable assumption in this case?

Bleaching Agents RecallthatDS9.3.4containstheresultsofanexperiment tocomparethebleachingeffectivenessoftwolevelsofhydrogenperoxide,alowlevelandahighlevel.Usetherank sumtesttoassesswhetherthereisevidenceofadifference between the low and high levels of hydrogen peroxide.

Clinical Trial Use the rank sum test to analyze the clinical trial data in DS 9.3.6.

Carbon Footprints Use the methods discussed in this chapter to analyze the data in DS 9.7.14, which contains estimates of the pounds of carbon dioxide released when making several types of car, together with information on whether or not it is an SUV.

Green Management A company introduces green management techniques to make its manufacturing processes more environmentally friendly and to cut waste. DS 9.7.15 shows weekly data on the percentage of damaged inventory for 10 weeks before and 10 weeks after the implementation of the new techniques. Use the methods discussed in this chapter to assess how the green management policies have affected the amount of damaged inventory.

Data Warehouse Design Power consumption represents a large proportion of a data centers costs. A redesign was undertaken by a company in an attempt to reduce these costs by more efcient uses of its physical components such as its routers, hubs, and switches. The data in DS 9.7.16 shows monthly electricty costs as a percentage of the data centers total costs. Use a nonparametric procedure to investigate what the data indicate about the effectiveness of the new design.

Natural Gas Consumption DS 9.7.18 contains data on the total daily natural gas consumption for a region for both the summer time and the winter time. Use nonparametric statistical techniques to investigate whether the natural gas consumption patterns vary between summer and winter.

Use the Kruskal-Wallis test procedure to analyze the data in DS 11.1.1. (a) Find the ranks rij. (b) What are the average ranks r1, r2, and r3? (c) What is the value of the test statistic H? (d) Write down an expression for the p-value and use a computer package to evaluate it.

Use the Kruskal-Wallis test procedure to analyze the data in DS 11.1.2. (a) Find the ranks rij and the average ranks r1, r2, r3, and r4. (b) What is the value of the test statistic H? (c) Write down an expression for the p-value and use a computer package to evaluate it.

Infrared Radiation Readings The data set in DS 11.1.3 concerns the infrared radiation readings from an energy source measured by a particular meter with three different background radiation levels. (a) Use the Kruskal-Wallis test procedure to investigate whether the radiation readings are affected by the background radiation level. (b) Repeat the analysis using an analysis of variance table. (c) What assumptions are required for the Kruskal-Wallis test procedure? What assumptions are required for the F-test in the analysis of variance table? Which analysis method do you prefer?

Keyboard Layout Designs DS 11.1.4 contains the times taken to perform a task using three different keyboard layouts for the numerical keys. Use the Kruskal-Wallis test procedure to investigate whether the different layouts affect the time taken to perform a task.

Computer Assembly Methods DS 11.1.6 contains the assembly times of computers for three different assembly methods. Use the Kruskal-Wallis test procedure to investigate whether there is any evidence that one assembly method is any quicker than the other methods.

Use the Friedman test procedure to analyze the data in DS 11.2.1. (a) Find the ranks rij. (b) What are the average ranks r1, r2, and r3? (c) What is the value of the test statistic S? (d) Write down an expression for the p-value and use a computer package to evaluate it.

Use the Friedman test procedure to analyze the data in DS 11.2.2. (a) Find the ranks rij and the average ranks r1, r2, r3, and r4. (b) What is the value of the test statistic S? (c) Write down an expression for the p-value and use a computer package to evaluate it.

Calciner Comparisons The data set in DS 11.2.3 concerns the brightness measurements for b =7 batches of kaolin processed through k =3 calciners. (a) Use the Friedman test procedure to investigate whether the calciners are operating with different efciencies. (b) Repeat the analysis using an analysis of variance table. (c) What assumptions are required for the Friedman test procedure? What assumptions are required for the F-test in the analysis of variance table? Which analysis method do you prefer?

Radar Detection of Airborne Objects DS 11.2.4 contains distances at detection for three radar systems. Use the Friedman test procedure to investigate whether there is evidence of any difference between the radar systems.

Production Line Assembly Methods The data set in DS 11.2.6 concerns an experiment to compare three different assembly methods for an electric motor. Use the Friedman test procedure to investigate whether there is evidence of any difference between the three assembly methods.

Realtor Commissions DS 11.2.7 contains the commissions obtained by ve agents in a Realtor ofce. Use the Friedman test procedure to investigate whether there is evidence of any real difference in the performances of the agents.

Cleanliness Scores for Detergent Comparisons The data set in DS 11.2.8 concerns an experiment to compare four different formulations of a detergent. Use the Friedman test procedure to investigate whether there is evidence of any difference between the detergent formulations.

Durations of Investigatory Surgical Procedures Use the appropriate nonparametric methodology from this section to analyze the data in DS 11.1.8.

E. Coli Colonies in Riverwater Use the appropriate nonparametric methodology from this section to analyze the data in DS 11.1.9.

Groundwater Pollution Levels Use the appropriate nonparametric methodology from this section to analyze the data in DS 11.2.9.

Volatile Organic Carbon Emissions Volatile organic carbon emissions are measured at ve locations of an industrial facility on each of 10 days, and the data is given in DS 11.5.11. Use a nonparametric procedure to investigate whether there is there any evidence of a difference in the emissions rates at the ve locations.

Osteoporosis Patient Heights (a) Construct the empirical cumulative distribution function for the data set of adult male heights given in DS 6.7.4. (b) Draw 95% condence bands around the empirical cumulative distribution function. (c) Is it plausible that the heights are normally distributed with a mean of 70 inches and a standard deviation of 2 inches? (d) Is it plausible that the heights are normally distributed with a mean of 71 inches and a standard deviation of 1 inch? (e) Consider the null hypothesis that the median height is 70 inches. What statistic is used by the sign test procedure to test this null hypothesis? What is the p-value? (f) Test the null hypothesis in part (e) using the signed rank test. (g) Use the sign test, the signed rank test, and the t-test to obtain 95% condence intervals on the median (or mean) service time. What assumptions are required by these three test procedures? Do the assumptions seem appropriate? How would you summarize your results?

Bamboo Cultivation Construct the empirical cumulative distribution function for the data set of bamboo shoot heights given in DS 6.7.5. Draw 95% condence bands around the empirical cumulative distribution function. Analyze the median (or mean) shoot height using the sign test, the signed rank test, and the t-test. Is there any evidence that the median (or mean) shoot height is less than 35 cm? Which analysis method do you prefer? Summarize your conclusions.

Tire Tread Wear Use the sign test and the signed rank test to analyze the paired data set of tire wear given in DS 9.2.3. Do you nd any evidence of a difference between the two types of tires? Do you think that the analysis with the signed rank test is better than the analysis with the sign test? Compare your results with an analysis using the t-test. What can you say about the difference in average wear for the two types of tires?

Video Display Designs Use the sign test and the signed rank test to analyze the paired data set given in DS 9.7.1 concerning the assimilationofinformationfromvideomonitors.Doyou nd any evidence of a difference between the two color types? Compare your results with an analysis based upon the t-test. Summarize your conclusions.

Consumer Complaints Division Reorganization Recall that DS 9.7.4 contains data observations of waiting times for a consumer to speak to a company representative on a telephone complaints line both before and after a reorganization. (a) Make a plot of the empirical cumulative distribution functions of these two data sets. (b) What does a visual comparison of the two empirical cumulative distribution functions suggest about the difference between the distributions of the waiting times? (c) Use the Kolmogorov-Smirnov test to assess the evidence that the two distribution functions are different.Doesthereorganizationappeartohavebeen successfulinaffectingthetimestakentoanswercalls?

Bamboo Cultivation A researcher compares the bamboo shoot heights in DS 6.7.5 obtained under growing conditions A with the bamboo shoot heights in DS 9.7.3 obtained under growingconditionsB.Recallthatthegrowingconditions Ballowed10%moresunlightthangrowingconditionsA. (a) Make a plot of the empirical cumulative distribution functions of these two data sets. (b) What does a visual comparison of the two empirical cumulative distribution functions suggest about the difference between the distributions of the bamboo shoot heights under the two growing conditions? (c) Use the Kolmogorov-Smirnov test to assess the evidence that the two distribution functions are different. (d) Use the rank sum test to assess the evidence that the two distribution functions are different. Obtain a 95% condence interval for the difference between the median bamboo shoot heights for the two growing conditions. On what assumption is the rank sum test based? Do you think that it is a reasonable assumption in this case? (e) Compare the results of the rank sum test with an analysis using a two-sample t-test. Which test procedure do you prefer in this case?

Use the rank sum test to analyze the data set in Figure 9.24 concerning Example 53 on kudzu pulping. Let population A be without the addition of anthraquinone and population B be with the addition of anthraquinone. (a) Combine the two samples and rank the observations. (b) What is SA? (c) What is UA? (d) Is the value of UA consistant with the addition of anthraquinone increasing or decreasing the yield? (e) Use a computer package to nd a one-sided p-value for the null hypothesis H0 : A B versus the alternative hypothesis HA : A < B. (f) Are your conclusions from this analysis consistent with the analysis presented in Section 9.3.4 using the two-sample t-test?

Biaxial Nanowire Tests DS 11.5.1 contains Youngs modulus measurements for four different types of nanowires. Use the Kruskal-Wallis test procedure to investigate whether there is any evidence of a difference in the types of nanowires. (a) Find the ranks rij. (b) What are the average ranks r1, r2, r3, and r4? (c) What is the value of the test statistic H? (d) Write down an expression for the p-value and use a computer package to evaluate it.

Car Gas Efciencies The data set in DS 11.5.2 concerns the gas mileages of four cars. (a) Use the Kruskal-Wallis test procedure to investigate whether any of the cars are getting better gas mileages than the other cars. (b) Repeat this analysis using an analysis of variance table. (c) What assumptions are required for the Kruskal-Wallis test procedure? What assumptions are required for the F-test in the analysis of variance table? Which analysis method do you prefer?

Temperature Effect on Cement Curing Use the Friedman test procedure to analyze the data set in DS 11.5.3 concerning cement strengths. (a) Find the ranks rij. (b) What are the average ranks r1, r2, r3, r4, and r5? (c) What is the value of the test statistic S? (d) Write down an expression for the p-value and use a computer package to evaluate it.

Fertilizer Comparisons DS 11.5.4 contains the results of an experiment to compare ve fertilizers. Use the Friedman test procedure to investigate whether there is evidence of any difference between the fertilizers.

Red Blood Cell Adhesion to Endothelial Cells The data set in DS 11.5.5 concerns the reports of k =4 clinics for b =12 samples of blood. (a) Use the Friedman test procedure to investigate whether the clinics appear to be reporting similar results. (b) Repeat the analysis using an analysis of variance table. (c) What assumptions are required for the Friedman test procedure? What assumptions are required for the F-test in the analysis of variance table? Which analysis method do you prefer?

Soil Compressibility Tests Recall the data set of soil compressibility measurements given in DS 6.7.6. Construct the empirical cumulative distribution function for this data set. Use the sign test and the signed rank test to investigate whether the engineers can conclude that the average soil compressibility is no larger than 25.5.

Ocular Motor Measurements DS 9.7.5 contains the data from an experiment in which a group of 10 subjects had their ocular motor measurements recorded after they had been reading a book for an hour and also after they had been reading a computer screen for an hour. Use the sign test and the signed rank test to analyze the data set.

Engine Oil Viscosity Oil viscosity values obtained from two engines are given in DS 9.7.6. Use the rank sum test to assess whether there is any evidence that the engines have different effects on the oil viscosity.

Insertion Gains of Hearing Aids Data collected on the insertion gain of a hearing aid for a constant noise stimulus placed at the horizontal level of the ear of a subject, placed above the horizontal level, and placed below the horizontal level are shown in DS 11.5.6. Use the Kruskal-Wallis test to analyze this data set.

Air Resistance Drag for Road Vehicles Data from wind tunnel tests performed on models of four different vehicle designs are shown in DS 11.5.7. What conclusions can you draw from this data set about the drags of the four different designs using the Kruskal-Wallis test?

Leather Shrinkage Measurements The shrinkage measurements of leather for four different preparation methods are given in DS 11.5.8. What conclusions can you draw from this data set about the differences between the four different preparation methods using the Friedman test?

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Glass Fiber Reinforced Polymer Tensile Strengths Data set in DS 6.7.7.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Infant Blood Levels of Hydrogen Peroxide Data set in DS 6.7.8.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Paper Mill Operation of a Lime Kiln Data set in DS 6.7.9.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. River Salinity Levels Data set in DS 6.7.10.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Dew Point Readings from Coastal Buoys Data set in DS 6.7.11.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Brain pH Levels Data set in DS 6.7.12.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Silicon Dioxide Percentages in Ocean Floor Volcanic Glass Data set in DS 6.7.13.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Network Server Response Times Data set in DS 6.7.14.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Flowrates in Urban Sewer Systems Data set in DS 8.6.1.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Polymer Compound Densities Data set in DS 8.6.2.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Reinforced Cement Strengths Data set in DS 9.7.7.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Comparisons of Experimental Drug Therapies Data set in DS 9.7.8.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Rubber Seal Curing Methods Data set in DS 9.7.9.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Light and Dark Regimens for Plant Growth Data set in DS 9.7.10.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Joystick Design for Spinal Cord Injury Patients Data set in DS 9.7.11.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Ambient Air Carbon Monoxide Pollution Levels Data set in DS 9.7.12.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Sphygmomanometer and Finger Monitor Systolic Blood Pressure Measurements Data set in DS 9.7.13.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Metal Alloy Hardness Tests Data set in DS 11.5.9.

Use the appropriate nonparametric methodologies from this chapter to analyze the data sets. Aquatic Radon Levels Data set in DS 11.5.10.

Customer Churn Customer churn is a term used for the attrition of a companys customers. DS 9.7.17 contains information from an Internet service provider on the length of days that its customers were signed up before switching to another provider, and whether or not they were a returning customer (that is, whether or not they had previously had Internet service from the company). Use the techniques described in this chapter to analyze these data.

Mercury Levels in Coal DS 6.7.19 shows the mercury levels of coal samples that are taken periodically as the coal is mined further and further into the seam. Use the nonparametric methodologies described in this chapter to analyze this data set.