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statistics for experimentert
Introduction To Statistics And Data Analysis 5th Edition Roxy Peck, Chris Olsen, Jay L Devore - Solutions
15.20 The accompanying data resulted from a flammability study in which specimens of five different fabrics were tested to determine burn times.1 17.8 16.2 15.9 15.5 2 13.2 10.4 11.3 Fabric 3 11.8 11.0 9.2 10.0 4 16.5 15.3 14.1 15.0 13.9 5 13.9 10.8 12.8 11.7 MSTr 5 23.67 MSE 5 1.39 F 5 17.08
15.21 Do lizards play a role in spreading plant seeds? Some research carried out in South Africa would suggest so(“Dispersal of Namaqua Fig [Ficus cordata cordata] Seeds by the Augrabies Flat Lizard [Platysaurus broadleyi],”Journal of Herpetology [1999]: 328–330). The researchers collected
15.22 Samples of six different brands of diet or imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids(PAPUFA, in percent), resulting in the data shown in the accompanying table. (The data are fictitious, but the sample means agree with data
1. Each of the four accompanying graphs shows a dotplot of data from three separate random samples. For each of the four graphs, indicate whether you think that the basic assumptions for single-factor ANOVA are plausible. Write a sentence or two justifying your answer.
2. Each of the three accompanying graphs shows a dotplot of data from three separate random samples. For each of the three graphs, indicate whether you think that the three population means are probably not all the same, you think that the three population means might be the same, or you are unsure
3. Sample data for each of the three graphs in Step 2 are shown in the table at the bottom of the page. For each of the three graphs, carry out a single-factor ANOVA.Are the results of the F tests consistent with your answers in Step 2? Explain.
15.15 The paper “Trends in Blood Lead Levels and Blood Lead Testing among U.S. Children Aged 1 to 5 Years” (Pediatrics[2009]: e376–e385) gave data on blood lead levels (in mg/dL) for samples of children living in homes that had been classified either at low, medium, or high risk of lead
15.14 Leaf surface area is an important variable in plant gas-exchange rates. Dry matter per unit surface area(mg/cm3) was measured for trees raised under three different growing conditions. Let m1, m2, and m3 represent the mean dry matter per unit surface area for the growing conditions 1, 2, and
15.13 In an experiment to investigate the performance of four different brands of spark plugs intended for use on a 125-cc motorcycle, five plugs of each brand were tested, and the number of miles (at a constant speed)until failure was observed. A partially completed ANOVA table is given. Fill in
15.3 Employees of a certain state university system can choose from among four different health plans.Each plan differs somewhat from the others in terms of hospitalization coverage. Four random samples of recently hospitalized individuals were selected, each sample consisting of people covered by
15.4 The accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in the paper“Perceived Causes of Loneliness in Adulthood” (Journal of Social Behavior and Personality [2000]: 67–84). The social marginality score
15.5 The authors of the paper “Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth”(Pediatrics [2009]: 870–876) carried out an experiment to determine if restrictive labels on video games actually increased the attractiveness of the game for young game players.
15.6 The paper referenced in the previous exercise also gave data for 12- to 13-year-old girls. Data consistent with summary values in the paper are shown below.Do the data provide convincing evidence that the mean rating associated with the game description for 12- to 13-year-old girls is not the
15.7 The paper “Women’s and Men’s Eating Behavior Following Exposure to Ideal-Body Images and Text”(Communication Research [2006]: 507–529) describes an experiment in which 74 men were assigned at random to one of four treatments:1. Viewed slides of fit, muscular men 2. Viewed slides of
15.8 Can use of an online plagiarism-detection system reduce plagiarism in student research papers? The paper “Plagiarism and Technology: A Tool for Coping with Plagiarism”(Journal of Education for Business [2005]: 149–152) describes a study in which randomly selected research papers
15.9 The experiment described in Example 15.4 also gave data on change in body fat mass for men (“Growth Hormone and Sex Steroid Administration in Healthy Aged Women and Men,” Journal of the American Medical Association [2002]: 2282–2292). Each of 74 male subjects who were over age 65 was
15.10 The article “Compression of Single-Wall Corrugated Shipping Containers Using Fixed and Floating Text Platens” (Journal of Testing and Evaluation [1992]: 318–320) described an experiment in which several different types of boxes were compared with respect to compression strength(in
15.11 In the introduction to this chapter, we considered a study comparing three groups of college students(soccer athletes, nonsoccer athletes, and a control group consisting of students who did not participate in intercollegiate sports). The following table gives information on scores from the
15.12 The accompanying data on calcium content of wheat are consistent with summary quantities that appeared in the article “Mineral Contents of Cereal Grains as Affected by Storage and Insect Infestation” (Journal of Stored Products Research [1992]: 147–151). Four different storage times
14.15 ▼ Consider the dependent variable y 5 fuel efficiency of a car (mpg).a. Suppose that you want to incorporate type of car, with four categories (subcompact, compact, midsize, and large), into a regression model that also includes x1 5 age of car and x2 5 engine size.Define the necessary
13.29 Sea bream are one type of fish that are often raised in large fish farming enterprises. These fish are usually fed a diet consisting primarily of fish meal. The authors of the paper “Growth and Economic Profit of Gilthead Sea Bream (Sparus aurata, L.) Fed Sunflower Meal” (Aquaculture
CR13.3 The article “Fines Show Airline Problems” (USA Today, February 2, 2010) gave the accompanying data on the number of fines for violating FAA maintenance regulations assessed against each of the 25 U.S. airlines from 2004 to 2009.1 12 3 7 23 36 6 14 1 3 4 10 6 2 2 2 2 2 3 1 2 2 1 0 0a.
CR13.6 The accompanying graphical display appeared in USA Today (February 19, 2010). It is meant to be a pie chart, but an oval rather than a circle is used to represent the whole pie. Do you think this graph does a good job of conveying the proportion falling into each of the three response
CR13.7 The following quote describing 18- to 29-yearolds is from the article “Study: Millennial Generation More Educated, Less Employed” (USA Today, February 23, 2010): “38%have a tattoo (and half of those with tattoos have two to five; 18% have six or more).” These percentages were based
CR13.8 To raise revenues, many airlines now charge fees to check luggage. Suppose that the number of checked bags was recorded for each person in a random sample of 100 airline passengers selected before fees were imposed and also for each person in a random sample of 100 airline passengers
CR13.9 Consider the following data on y 5 number of songs stored on an MP3 player and x 5 number of months the user has owned the MP3 player for a sample of 15 owners of MP3 players.x y 23 486 35 747 2 81 28 581 5 117 32 728 23 445 10 128 4 61 26 476 1 35 8 121 13 266 9 126 5 141a. Construct a
CR13.10 Many people take ginkgo supplements advertised to improve memory. Are these over-the-counter supplements effective? In a study reported in the paper “Ginkgo for Memory Enhancement” (Journal of the American Medical Association [2002]: 835– 840), elderly adults were assigned at random
CR13.11 The Harvard University Institute of Politics surveys undergraduates across the United States annually.Responses to the question “When it comes to voting, do you consider yourself to be affiliated with the Democratic Party, the Republican Party, or are you Independent or unaffiliated with
CR13.12 The survey described in the previous exercise also asked the following question: “Please tell me whether you trust the President to do the right thing all of the time, most of the time, some of the time, or never. Use the data in the table on the next page and an appropriate hypothesis
8. After consulting with your partner, write a paragraph explaining why it is a good idea to include a model utility test (H0: b 5 0) as part of a regression analysis.
13.30 ● The article “Vital Dimensions in Volume Perception:Can the Eye Fool the Stomach?” (Journal of Marketing Research [1999]: 313– 326) gave the accompanying data on the dimensions of 27 representative food products (Gerber baby food, Cheez Whiz, Skippy Peanut Butter, and Ahmed’s
13.31 Investigators in northern Alaska periodically monitored radio-collared wolves in 25 wolf packs over 4 years, keeping track of the packs’ home ranges (“Population Dynamics and Harvest Characteristics of Wolves in the Central Brooks Range, Alaska,”Wildlife Monographs, [2008]: 1–25). The
13.32 An investigation of the relationship between x 5 traffic flow (thousands of cars per 24 hours) and y 5 lead content of bark on trees near the highway(mg/g dry weight) yielded the accompanying data. A simple linear regression model was fit, and the resulting estimated regression line was y⁄5
1. Construct a scatterplot of the given data. Does there appear to be a linear relationship between y 5 height and x 5 number of siblings?Height(y)Number of Siblings (x)Height(y)Number of Siblings (x)64.2 2 65.5 1 65.4 0 67.2 2 64.6 2 66.4 2 66.1 6 63.3 0 65.1 3 61.7 1
2. Compute the value of the correlation coefficient. Is the value of the correlation coefficient consistent with your answer from Step 1? Explain.
3. What is the equation of the least-squares line for these data?
4. Is the slope of the least-squares regression line from Step 3 equal to 0? Does this necessarily mean that there is a meaningful relationship between height and number of siblings in the population of female students at this university? Discuss this with your partner, and then write a few
5. For the population of all female students at the university, do you think it is reasonable to assume that the distribution of heights at each particular x value is approximately normal and that the standard deviation of the height distribution at each particular x value is the same? That is, do
6. Carry out the model utility test (H0: b 5 0). Explain why the conclusion from this test is consistent with your explanation in Step 4.
7. Would you recommend using the least-squares regression line as a way of predicting heights for women at this university? Explain.
CR13.13 The report “Undergraduate Students and Credit Cards in 2004” (Nellie Mae, May 2005) included information collected from individuals in a random sample of undergraduate students in the United States. Students were classified according to region of residence and whether or not they have
14.14 The article “The Value and the Limitations of High-Speed Turbo-Exhausters for the Removal of Tar-Fog from Carburetted Water-Gas” (Society of Chemical Industry Journal [1946]: 166–168) presented data on y 5 tar content (grains/100 ft 3) of a gas stream as a function of x1 5 rotor speed
14.4 The following statement appeared in the article“Dimensions of Adjustment Among College Women”(Journal of College Student Development [1998]: 364):Regression analyses indicated that academic adjustment and race made independent contributions to academic achievement, as measured by current
14.5 The authors of the paper “Predicting Yolk Height, Yolk Width, Albumen Length, Eggshell Weight, Egg Shape Index, Eggshell Thickness, Egg Surface Area of Japanese Quails Using Various Egg Traits as Regressors” (International Journal of Poultry Science [2008]: 85–88) used a multiple
14.6 According to the paper “Assessing the Validity of the Post-Materialism Index” (American Political Science Review [1999]: 649–664), it is possible to predict an individual’s level of support for ecology based on demographic and ideological characteristics. The multiple regression model
14.7 ▼ The article “The Influence of Temperature and Sunshine on the Alpha-Acid Contents of Hops” (Agricultural Meteorology [1974]: 375–382) used a multiple regression model to relate y 5 yield of hops to x1 5 average temperature (8C) between date of coming into hop and date of picking and
14.8 The article “Readability of Liquid Crystal Displays: A Response Surface” (Human Factors [1983]: 185–190)used a multiple regression model with four independent variables, where y 5 error percentage for subjects reading a fourdigit liquid crystal display x1 5 level of backlight sfrom 0 to
14.9 The article “Pulp Brightness Reversion: Influence of Residual Lignin on the Brightness Reversion of Bleached Sulfite and Kraft Pulps” (TAPPI [1964]: 653–662) proposed a quadratic regression model to describe the relationship between x 5 degree of delignification during the processing of
14.10 The relationship between yield of maize, date of planting, and planting density was investigated in the article “Development of a Model for Use in Maize Replant Decisions” (Agronomy Journal [1980]: 459–464).Let y 5 percent maize yield x1 5 planting date sdays after April 20d x2 5
14.11 Suppose that the variables y, x1, and x2 are related by the regression model y 5 1.8 1 .1x1 1 .8x2 1 ea. Construct a graph (similar to that of Figure 14.5)showing the relationship between mean y and x2 for fixed values 10, 20, and 30 of x1.b. Construct a graph depicting the relationship
14.3 A number of investigations have focused on the problem of assessing loads that can be manually handled in a safe manner. The article “Anthropometric, Muscle Strength, and Spinal Mobility Characteristics as Predictors in the Rating of Acceptable Loads in Parcel Sorting”(Ergonomics [1992]:
14.2 The authors of the paper “Weight-Bearing Activity during Youth Is a More Important Factor for Peak Bone Mass than Calcium Intake” (Journal of Bone and Mineral Density [1994]: 1089–1096) used a multiple regression model to describe the relationship between y 5 bone mineral density sgycm3d
14.1a. Explain the difference between a deterministic and a probabilistic model.b. Give an example of a dependent variable y and two or more independent variables that might be related to y deterministically.c. Give an example of a dependent variable y and two or more independent variables that
CR13.14 The report described in the previous exercise also classified students according to region of residence and whether or not they had a credit card with a balance of more than $7000. Do these data support the conclusion that there is an association between region of residence and whether or
CR13.15 The discharge of industrial wastewater into rivers affects water quality. To assess the effect of a particular power plant on water quality, 24 water specimens were taken 16 km upstream and 4 km downstream of the plant.Alkalinity (mg/L) was determined for each specimen, resulting in the
CR13.16 The report of a European commission on radiation protection titled “Cosmic Radiation Exposure of Aircraft Crew” (2004) measured the exposure to radiation on eight international flights from Madrid using several different methods for measuring radiation. Data for two of the methods are
CR13.17 It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff. To test this, 120 pigeons are disoriented and released, and the direction of flight of each is recorded. The resulting data are given
●● how a multiple regression model can be used to model the relationship between a dependent variable and multiple independent variables.
●● how numerical and categorical independent variables can be incorporated into a multiple regression model.
●● the concept of interaction in a multiple regression setting.Students will be able to:
●● interpret the parameters of the multiple linear regression model in context.
●● use both numerical and categorical variables in a multiple regression model.
●● estimate the parameters in a multiple regression model and assess the usefulness of the model.
●● distinguish between paired and independent samples.●● carry out a test for a difference in population means using independent samples or paired samples and interpret the results in context.●● carry out a test for a difference in population proportions and interpret the results in
●● the difference between paired and independent samples.Students will be able to:
CR10.13 In an AP-AOL sports poll (Associated Press, December 18, 2005), 272 of 394 randomly selected baseball fans stated that they thought the designated hitter rule should either be expanded to both baseball leagues or eliminated.Based on the given information, is there sufficient evidence to
CR10.11 “Heinz Plays Catch-up After Under-Filling Ketchup Containers” is the headline of an article that appeared on CNN.com (November 30, 2000). The article stated that Heinz had agreed to put an extra 1% of ketchup into each ketchup container sold in California for a 1-year period. Suppose
CR10.6 The article “Should Canada Allow Direct-to-Consumer Advertising of Prescription Drugs?” (Canadian Family Physician[2009]: 130–131) calls for the legalization of advertising of prescription drugs in Canada. Suppose you wanted to conduct a survey to estimate the proportion of Canadians
CR10.4 The article “Wait Times on Rise to See Doctor”(USA Today, June 4, 2009) gave the accompanying data on average wait times in days to get an appointment with a medical specialist in 15 U.S. cities. Construct a boxplot of the average wait-time data. Are there any outliers in the data
CR10.3 The article “Flyers Trapped on Tarmac Push for Rules on Release” (USA Today, July 28, 2009) included the accompanying data on the number of flights with a tarmac delay of more than 3 hours between October 2008 and May 2009 for U.S. airlines.Airline Number of Flights Rate per 100,000
CR10.2 The following graphical display is similar to one that appeared in USA Today (June 3, 2009). Write a few sentences critiquing this graphical display. Do you think it does a good job of creating a visual representation of the three percentages in the display?
10.81 A student organization uses the proceeds from a particular soft-drink dispensing machine to finance its activities. The price per can had been $0.75 for a long time, and the average daily revenue during that period was $75.00. The price was recently increased to $1.00 per can. A random sample
10.80 An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry out a fuel efficiency test.Six nonprofessional drivers were selected, and each one drove a car from Phoenix to Los Angeles. The resulting fuel efficiencies (in miles
10.79 Past experience has indicated that the true response rate is 40% when individuals are approached with a request to fill out a questionnaire and return it in a stamped and addressed envelope. An investigator believes that if the person distributing the questionnaire is stigmatized in some
10.73 A number of initiatives on the topic of legalized gambling have appeared on state ballots. A political candidate has decided to support legalization of casino gambling if he is convinced that more than two-thirds of U.S. adults approve of casino gambling.Suppose that 1523 adults selected at
10.72 The authors of the article “Perceived Risks of Heart Disease and Cancer Among Cigarette Smokers”(Journal of the American Medical Association [1999]:1019–1021) expressed the concern that a majority of smokers do not view themselves as being at increased risk of heart disease or cancer. A
6. Now use the histograms from Step 5 to answer the following questions:a. Write a brief description of the shape, center, and spread for the histogram of the z values. Is what you see in the histogram consistent with what you would have expected to see? Explain. (Hint: In theory, what is the
5. Graphs, at last! Now construct histograms of the 200 z values and the 200 t values. These two graphical displays will provide insight about how each of these two statistics behaves in repeated sampling. Use the same scale for the two histograms so that it will be easier to compare the two
4. Now calculate the value of the t statistic for each of the 200 samples. Use the calculator function of Minitab to compute t 5 x 2 m ss/Ïnd 5x 2 100 ss/Ï5d as follows:Calc → Calculator In the “Store results in” box, enter c11 In the “Expression box” type in the following:
3. Next, calculate the value of the z statistic for each of the 200 samples. We can calculate z in this example because we know that the samples were selected from a population for which s 5 10. Use the calculator function of Minitab to compute z 5 x 2 m ss/Ïnd 5x 2 100 s10/Ï5d as follows:Calc
10.67 The article “Boy or Girl: Which Gender Baby Would You Pick?” (LiveScience, March 23, 2005, www.livescience.com) summarized the findings of a study that was published in Fertility and Sterility. The LiveScience article makes the following statements: “When given the opportunity to choose
10.66 In 2006, Boston Scientific sought approval for a new heart stent (a medical device used to open clogged arteries) called the Liberte. This stent was being proposed as an alternative to a stent called the Express that was already on the market. The following excerpt is from an article that
10.65 Let m denote the mean diameter for bearings of a certain type. A test of H0: m 5 0.5 versus Ha: m Þ0.5 will be based on a sample of n bearings. The diameter distribution is believed to be normal.Determine the value of b in each of the following cases:a. n 5 15, a 5 .05, s 5 0.02, m 5 0.52b.
10.64 Optical fibers are used in telecommunications to transmit light. Suppose current technology allows production of fibers that transmit light about 50 km.Researchers are trying to develop a new type of glass fiber that will increase this distance. In evaluating a new fiber, it is of interest to
10.63 The amount of shaft wear after a fixed mileage was determined for each of seven randomly selected internal combustion engines, resulting in a mean of 0.0372 inch and a standard deviation of 0.0125 inch.a. Assuming that the distribution of shaft wear is normal, Use a 5 .05 to test the
10.62 The city council in a large city has become concerned about the trend toward exclusion of renters with children in apartments within the city. The housing coordinator has decided to select a random sample of 125 apartments and determine for each whether children are permitted. Let p be the
10.61 ▼ Let m denote the true average lifetime (in hours)for a certain type of battery under controlled laboratory conditions. A test of H0: m 5 10 versus Ha:m , 10 will be based on a sample of size 36.Suppose that s is known to be 0.6, from which sx 5 .1. The appropriate test statistic is then z
10.60 Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 1508F, there will be no negative effects on the river’s ecosystem. To investigate
10.58 Much concern has been expressed regarding the practice of using nitrates as meat preservatives. In one study involving possible effects of these chemicals, bacteria cultures were grown in a medium containing nitrates. The rate of uptake of radio-labeled amino acid (in dpm, disintegrations per
10.57 ▼ Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of n 5 12 frozen dinners of a certain type was selected from production during a particular
10.54 A comprehensive study conducted by the National Institute of Child Health and Human Development tracked more than 1000 children from an early age through elementary school (New York Times, November 1, 2005). The study concluded that children who spent more than 30 hours a week in child care
10.52 Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at Cornell University used a proposed new computer mouse design. While using the mouse, each student’s wrist extension was recorded. Data consistent
10.51 A credit bureau analysis of undergraduate students’credit records found that the average number of credit cards in an undergraduate’s wallet was 4.09(“Undergraduate Students and Credit Cards in 2004,”Nellie Mae, May 2005). It was also reported that in a random sample of 132
10.50 ● The Economist collects data each year on the price of a Big Mac in various countries around the world.The price of a Big Mac for a sample of McDonald’s restaurants in Europe in January 2014 resulted in the following Big Mac prices (after conversion to U.S. dollars):5.18 4.95 4.07 4.68
10.48 A study of fast-food intake is described in the paper“What People Buy From Fast-Food Restaurants”(Obesity [2009]: 1369–1374). Adult customers at three hamburger chains (McDonald’s, Burger King, and Wendy’s) at lunchtime in New York City were approached as they entered the restaurant
10.47 The paper “Playing Active Video Games Increases Energy Expenditure in Children” (Pediatrics [2009]:534–539) describes an interesting investigation of the possible cardiovascular benefits of active video games. Mean heart rate for healthy boys age 10 to 13 after walking on a treadmill at
10.46 The true average diameter of ball bearings of a certain type is supposed to be 0.5 inch. What conclusion is appropriate when testing H0: m 5 0.5 versus Ha: m ? 0.5 inch each of the following situations:a. n 5 13, t 5 1.6, a 5 .05b. n 5 13, t 5 21.6, a 5 .05c. n 5 25, t 5 22.6, a 5 .01d. n 5
10.45 A certain pen has been designed so that true average writing lifetime under controlled conditions(involving the use of a writing machine) is at least 10 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting
10.44 Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let m denote the mean reflectometer reading for a new type of paint under consideration. A test of H0: m 5 20 versus Ha: m . 20 based on a sample of 15 observations gave t 5 3.2. What conclusion is
10.43 Give as much information as you can about the P-value of a t test in each of the following situations:a. Two-tailed test, df 5 9, t 5 0.73b. Upper-tailed test, df 5 10, t 5 20.5c. Lower-tailed test, n 5 20, t 5 22.1d. Lower-tailed test, n 5 20, t 5 25.1e. Two-tailed test, n 5 40, t 5 1.7
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