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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions

In Exercise 10.6, we reported the estimated average prices for a 6-ounce can or a 7.06-ounce pouch of tuna fish, based on prices paid nationally for a variety of different brands of tuna.1a. Use an analysis of variance for a completely randomized design to determine if there are significant
A national home builder wants to compare the prices per 1000 board feet of standard or better grade green Douglas fir framing lumber. He randomly selects five suppliers in each of the four states where the builder is planning to begin construction. The prices are given in the table.a. What type of
Twenty third graders were randomly separated into four equal groups, and each group was taught a mathematical concept using a different teaching method. At the end of the teaching period, progress was measured by a unit test. The scores are shown below (one child in group 3 was absent on the day
The values of Total SS and SSE for the experiment in Exercise 11.1 are Total SS = 21.4 and SSE = 16.2. a. Complete the ANOVA table for Exercise 11.1. b. How many degrees of freedom are associated with the F statistic for testing H0: μ1 - μ2 = μ6? c. Give the rejection region for the test in part
Consult Tables 11(a) and 11(b) in Appendix I and find the values of qa(k, df) for these cases: a. α = .05, k = 5, df = 7 b. α = .05, k = 3, df = 10 c. α = .01, k = 4, df = 8 d. α = .01, k = 7, df = 5
An independent random sampling design was used to compare the means of six treatments based on samples of four observations per treatment. The pooled estimator of σ2 is 9.12, and the sample means follow: 1 = 101.6 2 = 98.4 3 = 112.3 4 = 92.9 5 = 104.2 6 = 113.8 a. Give the value of v
Refer to Exercise 11.13 and data set EX1113. Rank the mean leaf growth for the four locations. Use a = .01.In Exercise 11.13 and data set EX1113
Refer to Exercise 11.15 and data set EX1115. The paired comparisons option in MINITAB generated the output provided here. What do these results tell you about the differences in the population means? Does this confirm your conclusions in Exercise 11.15?MINITAB output for Exercise 11.24Tukey's 95%
Physicians depend on laboratory test results when managing medical problems such as diabetes or epilepsy. In a uniformity test for glucose tolerance, three different laboratories were each sent nt = 5 identical blood samples from a person who had drunk 50 milligrams (mg) of glucose dissolved in
The analysis of variance F-test in Exercise 11.17 (and data set EX1117) determined that there was indeed a difference in the average cost of lumber for the four states. The following information from Exercise 11.17 is given in the table:Use Tukey's method for paired comparisons to determine which
The quantitative reasoning scores on the Graduate Record Examination (GRE)2 were recorded for students admitted to three different graduate programs at a local university.a. Do these data provide sufficient evidence to indicate a difference in the mean GRE scores for applicants admitted to the
A randomized block design was used to compare the means of three treatments within six blocks. Construct an ANOVA table showing the sources of variation and their respective degrees of freedom.
Suppose that the analysis of variance calculations for Exercise 11.28 are SST = 11.4, SSB = 17.1, and Total SS = 42.7. Complete the ANOVA table, showing all sums of squares, mean squares, and pertinent F-values.
The sample means corresponding to populations 1 and 2 in Exercise 11.1 are 1 = 3.07 and 2 = 2.52. a. Find a 95% confidence interval for μ1. b. Find a 95% confidence interval for the difference (μ1 - μ2).
Do the data of Exercise 11.28 provide sufficient evidence to indicate differences among the treatment means? Test using a = .05.
Refer to Exercise 11.28. Find a 95% confidence interval for the difference between a pair of treatment means A and B if A = 21.9 and B = 24.2.
Do the data of Exercise 11.28 provide sufficient evidence to indicate that blocking increased the amount of information in the experiment about the treatment means? Justify your answer.
The data that follow are observations collected from an experiment that compared four treatments, A, B, C, and D, within each of three blocks, using a randomized block design.a. Do the data present sufficient evidence to indicate differences among the treatment means? Test using a = .05.b. Do the
The data shown here are observations collected from an experiment that compared three treatments, A, B, and C, within each of five blocks, using a randomized block design:MS Excel output for Exercise 11.34 Use the Excel ouput to analyze the experiment. Investigate possible differences in the block
The partially completed ANOVA table for a randomized block design is presented here:a. How many blocks are involved in the design? b. How many observations are in each treatment total? c. How many observations are in each block total? d. Fill in the blanks in the ANOVA table. e. Do the data present
A study was conducted to compare automobile gasoline mileage for three formulations of gasoline. Four automobiles, all of the same make and model, were used in the experiment, and each formulation was tested in each automobile. Using each formulation in the same automobile has the effect of
An experiment was conducted to compare the effects of four different chemicals, A, B, C, and D, in producing water resistance in textiles. A strip of material, randomly selected from a bolt, was cut into four pieces, and the four pieces were randomly assigned to receive one of the four chemicals,
An experiment was conducted to compare the glare characteristics of four types of automobile rearview mirrors. Forty drivers were randomly selected to participate in the experiment. Each driver was exposed to the glare produced by a headlight located 30 feet behind the rear window of the
An experiment was conducted to determine the effects of three methods of soil preparation on the first-year growth of lash pine seedlings. Four locations (state forest lands) were selected, and each location was divided into three plots. Since it was felt that soil fertility within a location was
Suppose you wish to compare the means of four populations based on independent random samples, each of which contains six observations. Insert, in an ANOVA table, the sources of variation and their respective degrees of freedom.
A study was conducted to compare the effects of three levels of digitalis on the levels of calcium in the heart muscles of dogs. Because general level of calcium uptake varies from one animal to another, the tissue for a heart muscle was regarded as a block, and comparisons of the three digitalis
A building contractor employs three construction engineers, A, B, and C, to estimate and bid on jobs. To determine whether one tends to be a more conservative (or liberal) estimator than the others, the contractor selects four projected construction jobs and has each estimator independently
The cost of auto insurance varies by coverage, location, and the driving record of the driver. The following are estimates of the annual cost for standard coverage as of January 1, 2011 for a male driver with 6-8 years of experience, driving a Honda Accord with no accidents or violations.3 (These
Do you shop at the grocery store closest to home or do you look for the store that has the best prices? We compared the regular prices at four different grocery stores for eight items purchased on the same day.a. What are the blocks and treatments in this experiment? b. Do the data provide evidence
Refer to Exercise 11.43. The printout that follows provides the average costs of the selected items for the k = 4 stores. Store Mean Vons................... 4.1350 Ralphs................... 4.3400 Stater................... 3.8525 WinCo................... 2.5975 a. What is the appropriate
Suppose you were to conduct a two-factor factorial experiment, factor A at four levels and factor B at five levels, with three replications per treatment. a. How many treatments are involved in the experiment? b. How many observations are involved? c. List the sources of variation and their
The analysis of variance table for a 3 Ã— 4 factorial experiment, with factor A at three levels and factor B at four levels, and with two observations per treatment, is shown here:a. Fill in the missing items in the table. b. Do the data provide sufficient evidence to indicate that
Refer to Exercise 11.46. The means of two of the factor level combinations-say, A1B1 and A2B1 - are 1 = 8.3 and 2 = 6.3, respectively. Find a 95% confidence interval for the difference between the two corresponding population means.In Exercise 11.46.
The table gives data for a 3 Ã— 3 factorial experiment, with two replications per treatment:a. Perform an analysis of variance for the data, and present the results in an analysis of variance table. b. What do we mean when we say that factors A and B interact? c. Do the data provide
The table gives data for a 2 Ã— 2 factorial experiment, with four replications per treatment.a. The accompanying graph was generated by MINITAB. Verify that the four points that connect the two lines are the means of the four observations within each factor level combination. What does the graph
The values of Total SS and SST for the experiment in Exercise 11.4 are Total SS = 473.2 and SST = 339.8. a. Complete the ANOVA table for Exercise 11.4. b. How many degrees of freedom are associated with the F statistic for testing H0: μ1 = μ2 = μ3 = μ4? c. Give the rejection region for the test
A chain of jewelry stores conducted an experiment to investigate the effect of price markup and location on the demand for its diamonds. Six small-town stores were selected for the study, as well as six stores located in large suburban malls. Two stores in each of these locations were assigned to
A study was conducted to determine the effect of two factors on terrain visualization training for soldiers.4 During the training programs, participants viewed contour maps of various terrains and then were permitted to view a computer reconstruction of the terrain as it would appear from a
To explore ways to increase the educational experience using animation versus static images in a learning environment, Cyril Rebetez and colleagues5 ran a factorial experiment that measured retention of information under four factorial conditions: with animation or without animation; and
Fourth-Grade Test Scores A local school board was interested in comparing test scores on a standardized reading test for fourth-grade students in their district. They selected a random sample of five male and five female fourth grade students at each of four different elementary schools in the
An experiment was conducted to investigate the effect of management training on the decision-making abilities of supervisors in a large corporation. Sixteen supervisors were selected, and eight were randomly chosen to receive managerial training. Four trained and four untrained supervisors were
Refer to Exercise 11.54. The data for this experiment are shown in the table.a. Construct the ANOVA table for this experiment.b. Is there a significant interaction between the presence or absence of training and the type of decision making situation? Test at the 5% level of significance.c. Do the
Twenty-seven people participated in an experiment to compare the effects of five different stimuli on reaction time. The experiment was run using a completely randomized design, and, regardless of the results of the analysis of variance, the experimenters wanted to compare stimuli A and D. The
Refer to Exercise 11.56. Use this MINITAB output to identify the differences in the treatment means.MINITAB output for Exercise 11.57Tukey 95% Simultaneous Confidence IntervalsAll Pair wise Comparisons among Levels of StimulusIndividual confidence level = 99.29%Stimulus = A subtracted from:
Refer to Exercise 11.56. What do the normal probability plot and the residuals versus fit plot tell you about the validity of your analysis of variance results?MINITAB diagnostic plots for Exercise 11.58
The experiment in Exercise 11.56 might have been conducted more effectively using a randomized block design with people as blocks, since you would expect mean reaction time to vary from one person to another. Hence, four people were used in a new experiment, and each person was subjected to each of
The sample means corresponding to populations 1 and 2 in Exercise 11.4 are 1 = 88.0 and 2 = 83.9. a. Find a 90% confidence interval for μ1. b. Find a 90% confidence interval for the difference (μ1 - μ2).
An experiment was conducted to examine the effect of age on heart rate when a person is subjected to a specific amount of exercise. Ten male subjects were randomly selected from four age groups: 10-19, 20-39, 40-59, and 60-69. Each subject walked on a treadmill at a fixed grade for a period of 12
A company wished to study the effects of four training programs on the sales abilities of their sales personnel. Thirty-two people were randomly divided into four groups of equal size, and each group was then subjected to one of the different sales training programs. Because there were some
Suppose you were to conduct a two-factor factorial experiment, factor A at four levels and factor B at two levels, with r replications per treatment. a. How many treatments are involved in the experiment? b. How many observations are involved? c. List the sources of variation and their respective
The analysis of variance for a 2 Ã— 3 factorial experiment, factor A at two levels and factor B at three levels, with five observations per treatment, is shown in the table.a. Do the data provide sufficient evidence to indicate an interaction between factors A and B? Test using a =
Refer to Exercise 11.63. The means of all observations, at the factor A levels A1 and A2 are 1 = 3.7 and 2 = 1.4, respectively. Find a 95% confidence interval for the difference in mean response for factor levels A1 and A2.In Exercise 11.63
The whitefly, which causes defoliation of shrubs and trees and a reduction in salable crop yields, has emerged as a pest in Southern California. In a study to determine factors that affect the life cycle of the whitefly, an experiment was conducted in which whiteflies were placed on two different
Four chemical plants, producing the same product and owned by the same company, discharge effluents into streams in the vicinity of their locations. To check on the extent of the pollution created by the effluents and to determine whether this varies from plant to plant, the company collected
Exercise 10.41 examined an advertisement for a popular supermarket chain that claimed it has had consistently lower prices than one of its competitors. As part of a survey conducted by an independent price-checking company, the average weekly total, based on the prices of approximately 95 items, is
The yields of wheat (in bushels per acre) were compared for five different varieties, A, B, C, D, and E, at six different locations. Each variety was randomly assigned to a plot at each location. The results of the experiment are shown in the accompanying table, along with a MINITAB printout of the
Researchers Russell R. Pate and colleagues analyzed the results of the National Health and Nutrition Examination Survey to assess cardio respiratory fitness levels in youth aged 12 to 19 years.6 Estimated maximum oxygen uptake (VO2max) was used to measure a person's cardio respiratory level. The
These data are observations collected using a completely randomized design:a. Calculate CM and Total SS. b. Calculate SST and MST. c. Calculate SSE and MSE. d. Construct an ANOVA table for the data. e. State the null and alternative hypotheses for an analysis of variance F-test. f. Use the p-value
Professor's Salaries In a study of starting salaries of assistant professors,7 five male and five female beginning assistant professors at each of two types of institutions granting doctoral degrees were polled and their initial starting salaries were recorded. The results of the survey in
An article in Archaeometry involved an analysis of 26 samples of Romano-British pottery, found at four different kiln sites in the United Kingdom.8 Since one site only yielded two samples, consider the samples found at the other three sites. The samples were analyzed to determine their chemical
A smart phone is a mobile phone that offers more advanced computing ability and connectivity than a contemporary basic "feature phone." The data that follow are the ratings for six smart phones from each of the four suppliers, three of which cost $150 or more and three of which cost less than
The U.S. Department of Education7 reports the salaries of professors at universities and colleges in the United States. The following data (in thousands of dollars) is adapted from the report for full-time faculty on 9-month contracts at not-for-profit institutions offering doctoral programs. Ten
Refer to Exercise 11.7 and data set EX1107. Do the data provide sufficient evidence to indicate a difference between Î¼2 and Î¼3? Test using the t-test of Section 10.4 with a = .05.In Exercise 11.7 and data set EX1107
Refer to Exercise 11.7 and data set EX1107.a. Find a 90% confidence interval for m1.b. Find a 90% confidence interval for the difference (Î¼2 - Î¼3).In Exercise 11.7 and data set EX1107.
Canning or freezing produce that you buy in bulk will almost always save you money compared to buying in supermarkets. You can save more than 75% by canning-and more than 80% by freezing-produce purchased in bulk. The following prices are found in "Save Money on Groceries," an article by Roberta R.
Graph the line corresponding to the equation y + 2x + 1 by graphing the points corresponding to x = 0, 1, and 2. Give the y-intercept and slope for the line.
Using a chemical procedure called differential pulse polarography, a chemist measured the peak current generated (in microamperes) when a solution containing a given amount of nickel (in parts per billion) is added to a buffer:2 a. Use the data entry method for your calculator to calculate the
A study was conducted to determine the effects of sleep deprivation on people's ability to solve problems without sleep. A total of 10 subjects participated in the study, two at each of five sleep deprivation levels-8, 12, 16, 20, and 24 hours. After his or her specified sleep deprivation period,
Refer to the data given in the sleep deprivation experiment in Exercise 12.11. Answer the questions posed in parts a, b, d, and e of that exercise by completing the following MS Excel printout:
Tests The Academic Performance Index (API) is a measure of school achievement based on the results of the Stanford 9 Achievement test. Scores range from 200 to 1000, with 800 considered a long-range goal for schools. The following table shows the API for eight elementary schools in Riverside
How good are you at estimating? To test a subject's ability to estimate sizes, he was shown 10 different objects and asked to estimate their length or diameter. The object was then measured, and the results were recorded in the table below.a. Find the least-squares regression line for predicting
Of two personnel evaluation techniques available, the first requires a two-hour test interview while the second can be completed in less than an hour. The scores for each of the 15 individuals who took both tests are given in the next table.a. Construct a scatterplot for the data. Does the
Refer to Exercise 12.15. Construct the ANOVA table for the linear regression relating y, the score on Test 2, to x, the score on Test 1.In Exercise 12.15
Leonardo da Vinci (1452-1519) drew a sketch of a man, indicating that a person's arm span (measuring across the back with your arms outstretched to make a "T") is roughly equal to the person's height. To test this claim, we measured eight people with the following results:a. Draw a scatterplot for
The following data were obtained in an experiment relating the dependent variable, y (texture of strawberries), with x (coded storage temperature).a. Find the least-squares line for the data. b. Plot the data points and graph the least-squares line as a check on your calculations. c. Construct the
Refer to Exercise 12.6. The data are reproduced below.a. Do the data present sufficient evidence to indicate that y and x are linearly related? Test the hypothesis that Î² = 0 at the 5% level of significance. b. Use the ANOVA table from Exercise 12.6 to calculate F = MSR/MSE. Verify that
Graph the line corresponding to the equation y = -2x + 1 by graphing the points corresponding to x = 0, 1, and 2. Give the y-intercept and slope for the line. How is this line related to the line y = 2x + 1 of Exercise 12.1?
Refer to Exercise 12.19. Find a 95% confidence interval for the slope of the line. What does the phrase "95% confident" mean?In Exercise 12.19.
Refer to Exercise 12.7. The data, along with the MINITAB analysis of variance table are reproduced below.MINITAB ANOVA table for Exercise 12.21 a. Do the data provide sufficient evidence to indicate that y and x are linearly related? Use the information in the MINITAB printout to answer this
Refer to Exercise 12.8. The data, along with the MS Excel analysis of variance table are reproduced below:MS Excel ANOVA table for Exercise 12.22 a. Do the data provide sufficient evidence to indicate that y and x are linearly related? Use the information in the printout to answer this question at
In Exercise 3.18, we found that male crickets chirp by rubbing their front wings together, and their chirping is temperature dependent. The table below shows the number of chirps per second for a cricket, recorded at 10 different temperatures:a. Use the formulas given in this chapter to find the
The table below, a subset of the data given in Exercise 3.33, shows the gestation time in days and the average longevity in years for a variety of mammals in captivity.4a. If you want to estimate the average longevity of an animal based on its gestation time, which variable is the response variable
Refer to the data in Exercise 12.9, relating x, the number of books written by Professor Isaac Asimov, to y, the number of months he took to write his books (in increments of 100). The data are reproduced below.a. Do the data support the hypothesis that Î² = 0? Use the p-value approach,
Refer to the sleep deprivation experiment described in Exercises 12.11 and 12.12 and data set EX1211. The data and the MINITAB and MS Excel printout are reproduced here.MINITAB output for Exercise 12.26 Regression Analysis: y versus x The regression equation is y = 3.00 + 0.475 x MS Excel output
The following data (Exercise 12.18 and data set EX1218) were obtained in an experiment relating the dependent variable, y (texture of strawberries), with x (coded storage temperature). Use the information from Exercise 12.18 to answer the following questions:a. What is the best estimate of
In Exercise 1.61 we described an informal experiment conducted at McNair Academic High School in Jersey City, New Jersey. Two freshman algebra classes were studied, one of which used laptop computers at school and at home, while the other class did not. In each class, students were given a survey
Refer to Exercise 12.28. a. Use the MINITAB printout to find the value of the coefficient of determination, r2. Show that r2 = SSR/Total SS. b. What percentage reduction in the total variation is achieved by using the linear regression model?
In Exercise 12.17 (data set EX1217), we measured the arm span and height of eight people with the following results:a. Does the data provide sufficient evidence to indicate that there is a linear relationship between arm span and height? Test at the 5% level of significance. b. Construct a 95%
Refer to Exercise 12.9, in which the number of books x written by Isaac Asimov are related to the number of months y he took to write them. A plot of the data is shown.a. Can you see any pattern other than a linear relationship in the original plot? b. The value of r2 for these data is .959. What
Refer to the data given in Exercise 12.28. The MINITAB printout is reproduced here.Regression Analysis: y versus xThe regression equation isy = -26.8 + 1.26 xa. What assumptions must be made about the distribution of the random error, Îµ? b. What is the best estimate of Ïƒ2,
In Exercise 3.19, Consumer Reports6 gave the prices and screen sizes for the top 10 LCD TVs in the 46-inch and higher categories. Does the price of an LCD TV depend on the size of the screen?a. Suppose that we assume that the relationship between size and price is linear, and perform a linear
Refer to Exercise 12.6.a. Estimate the average value of y when x = 1, using a 90% confidence interval.b. Find a 90% prediction interval for some value of y to be observed in the future when x = 1.In Exercise 12.6.
Refer to Exercise 12.7. Portions of the MINITAB printout are shown here.MINITAB output for Exercise 12.40Regression Analysis: y versus xThe regression equation isy = 6.00 - 0.557 xa. Find a 95% confidence interval for the average value of y when x = 2.b. Find a 95% prediction interval for some
A marketing research experiment was conducted to study the relationship between the length of time necessary for a buyer to reach a decision and the number of alternative package designs of a product presented. Brand names were eliminated from the packages and the buyers made their selections using
The data in the table give the square footages and sales prices of n = 12 houses randomly selected from those sold in a small city. Use the MINITAB printout to answer the questions.Plot of data for Exercise 12.42MINITAB output for Exercise 12.42Regression Analysis: y versus xThe regression equation
Refer to Exercise 12.42 and data set EX1242.a. Estimate the average increase in the price for an increase of 1 square foot for houses sold in the city. Use a 99% confidence interval. Interpret your estimate.b. A real estate salesperson needs to estimate the average sales price of houses with a
The following data (Exercises 12.18 and 12.27) were obtained in an experiment relating the dependent variable, y (texture of strawberries), with x (coded storage temperature).a. Estimate the expected strawberry texture for a coded storage temperature of x = 1. Use a 99% confidence interval. b.
The number of passes completed and the total number of passing yards for Drew Brees, quarterback for the New Orleans Saints, were recorded for the 16 regular games in the 2010 football season.7 Week 10 was a bye and no data was reported.a. What is the least-squares line relating the total passing
Refer to Exercise 12.45.a. Estimate the average number of passing yards for games in which Brees throws 20 completed passes using a 95% confidence interval.b. Predict the actual number of passing yards for games in which Brees throws 20 completed passes using a 95% confidence interval.c. Would it
How does the coefficient of correlation measure the strength of the linear relationship between two variables y and x?

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