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business
essentials of statistics
The Basic Practice Of Statistics 5th Edition David S Moore - Solutions
Do good smells bring good business? Exercise 18.9 (text page 483) describes ST EP an experiment that asked whether background aromas in a restaurant encourage customers to stay longer and spend more. The data on amount spent (in euros) are as follows:No Odor 15.9 18.5 15.9 18.5 18.5 21.9 15.9 15.9
Tell me a story, continued. The data in Exercise 25.5 for a story told without pictures (Story 1) have tied observations. Is there good evidence that high-progress readers score higher than low-progress readers when they retell a story they have heard without pictures?(a) Make a back-to-back
Do birds learn to time their breeding? Exercises 18.42 to 18.44 (text pages 497–498) concern a study of whether supplementing the diet of blue titmice with extra caterpillars will prevent them from adjusting their breeding date the following year in search of a better food supply. Here are the
Does polyester decay? Exercise 18.8 (text page 482) compares the breaking strength of polyester strips buried for 16 weeks with that of strips buried for 2 weeks.The breaking strengths in pounds are 2 weeks 118 126 126 120 129 16 weeks 124 98 110 140 110(a) What are the null and alternative
Strength of durable press fabrics: hypotheses.We are interested in whether fabrics treated with the Permafresh and Hylite processes have the same breaking strength “on the average.”(a) State null and alternative hypotheses in terms of population means. What test would we typically use for these
Daily activity and obesity: hypotheses.We could use either two-sample t or the Wilcoxon rank sum to test the null hypothesis that lean and mildly obese people don’t differ in the time they spend standing and walking against the alternative hypothesis that lean people generally spend more time in
Weeds among the corn. The corn yield study of Example 25.1 also examined yields in four plots having 9 lamb’s-quarter plants per meter of row. The yields(bushels per acre) in these plots were 162.8 142.4 162.7 162.4 There is a clear outlier, but rechecking the results found that this is the
Daily activity and obesity: software. Use your software to carry out the onesidedWilcoxon rank sum test that you did by hand in Exercise 25.3. Use the exact distribution if your software will do it. Compare the software result with your result in Exercise 25.3.
Strength of durable press fabrics: software. Use your software to repeat the Wilcoxon test you did in Exercise 25.4. By comparing the results, state how your software finds P-values forW: exact distribution, Normal approximation with continuity correction, or Normal approximation without continuity
Tell me a story. A study of early childhood education asked kindergarten students ST EP to tell fairy tales that had been read to them earlier in the week. The 10 children in the study included 5 high-progress readers and 5 low-progress readers. Each child told two stories. Story 1 had been read to
Strength of durable press fabrics, continued. Use your values of W, μW, andσW from Exercise 25.2 to see whether fabrics treated with the two processes differ in breaking strength.(a) The two-sided P-value is 2P(W ≥ ?). Using the continuity correction, what number replaces the ? in this
Daily activity and obesity, continued. In Exercise 25.1, you found theWilcoxon rank sumWand its mean and standard deviation.We want to test the null hypothesis that the two groups don’t differ in activity against the alternative hypothesis that the lean subjects spend more time standing and
How strong are durable press fabrics? Exercise 18.38 (text page 496) describes an experiment comparing the strengths of cotton fabric treated with two “durable press” processes. Here are the breaking strengths in pounds:Permafresh 29.9 30.7 30.0 29.5 27.6 Hylite 28.8 23.9 27.0 22.1 24.2 There
Daily activity and obesity. Our lead example for the two-sample t procedures in Chapter 18 concerned a study comparing the level of physical activity of lean and mildly obese people who don’t exercise. Here are the minutes per day that the subjects spent standing or walking over a 10-day
Attitudes toward math. Do high school students from different racial/ethnic groups have different attitudes toward mathematics? Measure the level of interest in mathematics on a 5-point scale for a national random sample of students.Here are summaries for students who were taking math at the time
Exercise and weight loss. What conditions help overweight people exercise regularly?Subjects were randomly assigned to three treatments: a single long exercise period 5 days per week; several 10-minute exercise periods 5 days per week; and several 10-minute periods 5 days per week on a home
Road rage. Exercise 24.2 describes a study of road rage. Here are the means and standard deviations for a measure of “angry/threatening driving” for random samples of drivers in three age groups:Age group n x s Less than 30 years 244 2.22 3.11 30 to 55 years 734 1.33 2.21 Over 55 years 364 0.66
What music will you play? People often match their behavior to their social environment. One study of this idea first established that the type of music most preferred by black college students is R&B and that whites’ most preferred music is rock. Will students hosting a small group of other
Logging in the rain forest, continued. Exercise 24.3 compares the number of tree species in rain forest plots that had never been logged (Group 1) with similar plots nearby that had been logged 1 year earlier (Group 2) and 8 years earlier(Group 3).(a) What are I , the ni , and N for these data?
Fertilizing bromeliads. Bromeliads are tropical flowering plants. Many are epi-S TE Pphytes that attach to trees and obtain moisture and nutrients from air and rain.Their leaf bases form cups that collect water and are home to the larvae of many insects. As a preliminary to a study of changes in
Species richness after logging. Table 24.2 gives data on the species richness in rain forest plots, defined as the number of tree species in a plot divided by the number of trees in the plot. ANOVA may not be trustworthy for the richness data.Do data analysis: make side-by-side stemplots to examine
Checking standard deviations. Verify that the sample standard deviations for these sets of data do allow use of ANOVA to compare the population means.(a) The counts of trees in Exercise 24.3 and Figure 24.4.(b) The restaurant times of Exercise 24.4 and Figure 24.5.
ANOVA uses within-group variation. Reset the One-Way ANOVA applet to•••APPLET its original state. As in Figure 24.6(b), the differences among the three means are highly significant (large F , small P-value) because the observations in each group cluster tightly about the group mean.(a) Use
ANOVA compares several means. The One-Way ANOVA applet displays the APPLET ••• observations in three groups, with the group means highlighted by black dots.When you open or reset the applet, the scale at the bottom of the display shows that for these groups the ANOVA F statistic is F = 31.74,
Do good smells bring good business? Businesses know that customers often respond to background music. Do they also respond to odors? Nicolas Gu´eguen and his colleagues studied this question in a small pizza restaurant in France on Saturday evenings in May. On one evening, a relaxing lavender odor
Logging in the rain forest. How does logging in a tropical rain forest affect the forest in later years? Researchers compared forest plots in Borneo that had never been logged (Group 1) with similar plots nearby that had been logged 1 year earlier(Group 2) and 8 years earlier (Group 3). Although
Road rage. “The phenomenon of road rage has been frequently discussed but infrequently examined.” So begins a report based on interviews with 1382 randomly selected drivers.3 The respondents’ answers to interview questions produced scores on an “angry/threatening driving scale”with values
Choose your parents wisely. To live long, it helps to have long-lived parents.One study of this “inheritance of longevity”looked at records of families in a small mountain valley in France where the style of life changed little over time. Married couples in which both husband and wife were born
Growth of icicles: residuals. Figure 23.4 gives part of the Minitab output for the data on growth of icicles in Exercise 23.2. Figure 23.12 comes from another part of the output. It gives x, y, the predicted response ˆy, the residual y − ˆy, and related quantities for each of the 18
Crying and IQ: residuals. The residuals for the study of crying and IQ appear in Example 23.3.(a) Make a stemplot to display the distribution of the residuals (round to the nearest whole number). Are there strong outliers or other signs of departures from Normality?(b) Make a residual plot,
Growth of icicles: prediction. Analysis of the data in Exercise 23.2 shows that growth of icicles is very linear.We might want to predict the mean length of icicles after 200 minutes under the same conditions of temperature, wind, and water flow.Here is the Minitab output for prediction when x∗ =
Ebola and gorillas: prediction. Exercise 23.1 presents data on distance and days until an Ebola outbreak reached six groups of gorillas. If another group were located 2 ranges from the original outbreak, predict the number of days until deaths begin in this group.(a) Figure 23.8 is part of the
Great Arctic rivers: estimating slope. Use the data in Table 23.2 to give a 90%confidence interval for the slope of the population regression of Arctic river discharge on year. Does this interval convince you that discharge is actually increasing over time? Explain your answer.
Growth of icicles: estimating slope. Exercise 23.2 gives data on the growth of an icicle.We want a 95% confidence interval for the slope of the population regression line. Starting from the information in the Minitab output in Figure 23.4, find this interval. Say in words what the slope of the
Ebola and gorillas: estimating slope. Exercise 23.1 presents data on distance and days until an Ebola outbreak reached six groups of gorillas. Software tells us that the least-squares slope is b = 11.263 with standard error SEb = 1.591. Because there are only 6 observations, the observed slope b
Does social rejection hurt? Exercise 4.45 (page 122) gives data from a study of whether social rejection causes activity in areas of the brain that are known to be activated by physical pain. The explanatory variable is a subject’s score on a test of “social distress” after being excluded
Ebola and gorillas: testing correlation. Exercise 23.1 gives data showing that the delay in deaths from an Ebola outbreak in groups of gorillas increases linearly with distance from the origin of the outbreak. There are only 6 observations, so we worry that the apparent relationship may be just
Does fast driving waste fuel? Exercise 4.8 (page 102) gives data on the fuel consumption of a small car at various speeds from 10 to 150 kilometers per hour. Is there significant evidence of straight-line dependence between speed and fuel use?Make a scatterplot and use it to explain the result of
Great Arctic rivers: testing. The most important question we ask of the data in Table 23.2 is this: is the increasing trend visible in your plot (Exercise 23.3)statistically significant? If so, changes in the Arctic may already be affecting the earth’s climate. Use software to answer this
Ebola and gorillas: testing. Exercise 23.1 gives data on the distance of gorilla groups from the origin of an Ebola outbreak and the number of days until deaths from Ebola began. Software tells us that the least-squares slope is b = 11.263 with standard error SEb = 1.591.(a) What is the t statistic
Great Arctic rivers. One effect of global warming is to increase the flow of water into the Arctic Ocean from rivers. Such an increase may have major effects on the world’s climate. Six rivers (Yenisey, Lena, Ob, Pechora, Kolyma, and Severnaya Dvina) drain two-thirds of the Arctic in Europe and
How fast do icicles grow? The rate at which an icicle grows depends on temperature, water flow, and wind. The data below are for an icicle grown in a cold chamber at −11◦C with no wind and a water flow of 11.9 milligrams per second.3 Time (min) 10 20 30 40 50 60 70 80 90 Length (cm) 0.6 1.8 2.9
Ebola and gorillas. An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure “distance” by the number of home ranges separating a group of gorillas from the first group infected. Here are data on
What’s your sign? For reasons known only to social scientists, the General Social ST EP Survey (GSS) regularly asks its subjects their astrological sign. Here are the counts of responses for the most recent GSS:Sign Aries Taurus Gemini Cancer Leo Virgo Count 321 360 367 374 383 402 Sign Libra
Course grades. Most students in a large statistics course are taught by teaching assistants (TAs). One section is taught by the course supervisor, a senior professor.The distribution of grades for the hundreds of students taught by TAs this semester was Grade A B C D/F Probability 0.32 0.41 0.20
Police harassment? Police may use minor violations such as not wearing a seat belt to stop motorists for other reasons. A large study in Michigan first studied the population of drivers not wearing seat belts during daylight hours by observation at more than 400 locations around the state. Here is
More on birth days. Births really are not evenly distributed across the days of the week. The data in Example 22.8 failed to reject this null hypothesis because of random variation in a quite small number of births. Here are data on 700 births in the same locale:Day Sun. Mon. Tue. Wed. Thu. Fri.
Saving birds from windows. Many birds are injured or killed by flying into windows.It appears that birds don’t see windows. Can tilting windows down so that they reflect earth rather than sky reduce bird strikes? Place six windows at the edge of a woods: two vertical, two tilted 20 degrees, and
Attitudes toward recycled products. The Minitab output in Figure 22.4 gives 2 degrees of freedom for the table in Exercise 22.2.(a) Verify that this is correct.(b) The computer gives the value of the chi-square statistic as χ2 = 7.638. Between what two entries in Table D does this value lie?
Facebook at Penn State. The Minitab output in Figure 22.3 gives the degrees of freedom for a table of Facebook use by students at two campus locations as DF = 2.(a) Show that this is correct for a table with 3 rows and 2 columns.(b) Minitab gives the chi-square statistic as Chi-Sq = 19.489. Where
Cell-only versus landline users. We suspect that people who rely entirely on ST EP cell phones will as a group be younger than those who have a landline telephone.Do data confirm this guess? Here is a two-way table that breaks down both of Pew’s samples (see Example 22.6) by age group:Landline
Is astrology scientific? The General Social Survey asked a random sample of ST EP adults about their education and about their view of astrology as scientific or not.Here are the data for people with three levels of higher education:Degree Held Associate’s Bachelor’s Master’s Not at all
Attitudes toward recycled products. Your data analysis in Exercise 22.2 found that people who have bought recycled coffee filters tend to have more positive opinions about the filters than those who have not. Figure 22.4 gives Minitab output for the two-way table in Exercise 22.2.(a) Verify from
Facebook at Penn State. Figure 22.3 displays Minitab output for how frequently students at the University Park and commonwealth campuses of Penn State University who have Facebook accounts make use of their accounts. The output includes the two-way table of observed counts, the expected counts, and
Attitudes toward recycled products. Exercise 22.2 describes a comparison of the attitudes of people who do and don’t buy coffee filters made of recycled paper.The null hypothesis “no relationship” says that in the population of all consumers, the proportions who hold each attitude are the
Facebook at Penn State. The two-way table in Exercise 22.1 displays data on use of Facebook by two groups of Penn State students. It’s clear that nonusers are much more frequent at the commonwealth campuses. Let’s look just at students who have Facebook accounts:Use Facebook University Park
Is astrology scientific? The University of Chicago’s General Social Survey(GSS) is the nation’s most important social science sample survey. The GSS asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a
Facebook at Penn State. In the setting of Exercise 22.1, we might do several significance tests to compare University Park with the commonwealth campuses.(a) Is there a significant difference between the proportions of students in the two locations who do not use Facebook? Give the P-value.(b) Is
Attitudes toward recycled products. Some people think recycled products are lower in quality than other products, a fact that makes recycling less practical. Here are data on attitudes toward coffee filters made of recycled paper.3 Think the Quality of the Recycled Product Is Higher Same Lower
Facebook at Penn State. The Pennsylvania State University has its main campus in University Park and more than 20 smaller “commonwealth campuses” around the state. The Penn State Division of Student Affairs polled a random sample of undergraduates about their use of online social networking.
Shake your head. Our bodies affect our behavior in strange ways. Psychologists asked student subjects to either nod their heads up and down or shake their heads side to side while listening to music through headphones. The subjects thought that they were evaluating the headphones. An experimenter
Protecting skiers and snowboarders. Most alpine skiers and snowboarders do not use helmets. Do helmets reduce the risk of head injuries? A study in Norway compared skiers and snowboarders who suffered head injuries with a control group who were not injured. Of 578 injured subjects, 96 had worn a
Did the random assignment work? A large clinical trial of the effect of diet ST EP on breast cancer assigned women at random to either a normal diet or a low-fat diet. To check that the random assignment did produce comparable groups, we can compare the two groups at the start of the study. Ask if
Broken crackers. We don’t like to find broken crackers when we open the ST EP package. How can makers reduce breaking? One idea is to microwave the crackers for 30 seconds right after baking them. Breaks start as hairline cracks called“checking.” Assign 65 newly baked crackers to the
In-line skaters. A study of injuries to in-line skaters used data from the National Electronic Injury Surveillance System, which collects data from a random sample of hospital emergency rooms. The researchers interviewed 161 people who came to emergency rooms with injuries from in-line
High school students in action. A government survey randomly selected 6889 female high school students and 7028 male high school students.4 Of these students, 1915 females and 3078 males met recommended levels of physical activity.(These levels are quite high: at least 60 minutes of activity that
Listening to rap. Rap music is more popular among young blacks than among ST EP young whites. A sample survey compared 634 randomly chosen blacks aged 15 to 25 with 567 randomly selected whites in the same age group. It found that 368 of the blacks and 130 of the whites listened to rap music every
Who uses instant messaging? Younger people use online instant messaging ST EP(IM) more often than older people. A random sample of IM users found that 73 of the 158 people in the sample aged 18 to 27 said they used IM more often than email. In the 28 to 39 age group, 26 of 143 people used IM more
No test. Explain why we can’t use the z test for a proportion in these situations:(a) You toss a coin 10 times in order to test the hypothesis H0: p = 0.5 that the coin is balanced.(b) A college president says, “99% of the alumni support my firing of Coach Boggs.” You contact an SRS of 200 of
Vote for the best face? We often judge other people by their faces. It appears ST EP that some people judge candidates for elected office by their faces. Psychologists showed head-and-shoulders photos of the two main candidates in 32 races for the U.S. Senate to many subjects (dropping subjects who
Spinning pennies. Spinning a coin, unlike tossing it, may not give heads and tails ST EP equal probabilities. I spun a penny 200 times and got 83 heads. How significant is this evidence against equal probabilities? Follow the four-step process as illustrated in Example 19.7.
Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans with at least one Italian grandparent who can
Canadians and doctor-assisted suicide.AGallup Poll asked a sample of Canadian adults if they thought the law should allow doctors to end the life of a patient who is in great pain and near death if the patient makes a request in writing. The poll included 270 people in Qu´ebec, 221 of whom agreed
Cocaine traces in Spanish currency, continued. The plus four method is particularly useful when there are no successes or no failures in the data. The study of Spanish currency described in Example 19.5 found that in Seville, all 20 of a sample of 20 euro bills had cocaine traces.(a) What is the
Teens’ MySpace profiles. Over half of all American teens (ages 12 to 17 years)have an online profile, mainly on MySpace. A random sample of 487 teens with profiles found that 385 included photos of themselves.11(a) Give the 95% large-sample confidence interval for the proportion p of all teens
Whelks and mussels. Sample surveys usually contact large samples, so we can use the large-sample confidence interval if the sample design is close to an SRS.Scientific studies often use smaller samples that require the plus four method. For example, the small round holes you often see in sea shells
How common is SAT coaching? A random sample of students who took the ST EP SAT college entrance examination twice found that 427 of the respondents had paid for coaching courses and that the remaining 2733 had not.6 Give a 99% confidence interval for the proportion of coaching among students who
Canadian attitudes toward guns. Canada has much stronger gun control laws than the United States, and Canadians support gun control more strongly than do Americans. A sample survey asked a random sample of 1505 adult Canadians, “Do you agree or disagree that all firearms should be registered?”
No confidence interval. In the National AIDS Behavioral Surveys sample of 2673 adult heterosexuals, 0.2% (that’s 0.002 as a decimal fraction) had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS. Explain why we can’t use the large-sample confidence
Watching online video. About 75% of young adult Internet users (ages 18 to 29)watch online video. Suppose that a sample survey contacts an SRS of 1000 young adult Internet users and calculates the proportion ˆp in this sample who watch online video.(a) What is the approximate distribution of
Spam. Are you getting more spam in your personal email account? Suppose that 40% of adult email users would say “Yes.”A polling firm contacts an SRS of 1500 people chosen from this population. If the sample were repeated many times, what would be the range of sample proportions who say
Do college students pray? A study of religious practices among college students interviewed a sample of 127 students; 107 of the students said that they prayed at least once in a while.(a) Describe the population and explain in words what the parameter p is.(b) Give the numerical value of the
Students’ self-concept, continued. Write a sentence or two summarizing the comparison of female and male students in Exercise 18.13, as if you were preparing a report for publication. Use the output in Exercise 18.13.
Does polyester decay? Figure 18.5 gives output for the breaking strength data in Exercise 18.8 from software that does Option 1 with the correct degrees of freedom.What are xi and si for the two samples? Starting from these values, find the t test statistic and its degrees of freedom. Your work
Students’ self-concept. A study of the self-concept of seventh-grade students asked if male and female students differ in mean score on the Piers-Harris Children’s Self-Concept Scale.9 Software that uses Option 1 gives these summary results:Gender n Mean Std dev Std err t df P F 31 55.5161
Compressing soil, continued. Use the data in Exercise 18.10, omitting the outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil.
Weeds among the corn. Exercise 7.32 (page 189) gives these corn yields (bushels per acre) for experimental plots controlled to have 1 weed per meter of row and 3 weeds per meter of row:1 weed/meter 166.2 157.3 166.7 161.1 3 weeds/meter 158.6 176.4 153.1 156.0 Explain carefully why a two-sample t
Compressing soil. Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. Here are data on the “penetrability” of the same type of soil at two levels of compression.8 Penetrability is a measure of how much resistance plant roots will meet when they
Do good smells bring good business? Businesses know that customers often respond to background music. Do they also respond to odors? One study of this question took place in a small pizza restaurant in France on Saturday evenings in May. On one of these evenings, a relaxing lavender odor was spread
Does polyester decay? How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried 10 strips of polyester fabric in well-drained soil in the summer. Five of the strips, chosen at random, were dug up after 2 weeks; the other 5 were dug up after 16 weeks. Breaking
Logging in the rain forest, continued. Use the data in Exercise 18.5 to give a 90% confidence interval for the difference in mean number of species between unlogged and logged plots.
Daily activity and obesity. We can conclude from Examples 18.2 and 18.3 that ST EP mildly obese people spend less time standing and walking (on the average) than lean people. Is there a significant difference between the mean times the two groups spend lying down? Use the four-step process to
Logging in the rain forest. “Conservationists have despaired over destruction of S TE Ptropical rain forest by logging, clearing, and burning.” These words begin a report on a statistical study of the effects of logging in Borneo.4 Here are data on the number of tree species in 12 unlogged
Chemical analysis, continued. Another chemist is checking the same new method. He has no reference specimen, but a familiar analytic method is available.He wants to know if the new and old methods agree. He takes a specimen of unknown concentration and measures the concentration 10 times with the
Chemical analysis. To check a new analytical method, a chemist obtains a reference specimen of known concentration from the National Institute of Standards and Technology. She then makes 20 measurements of the concentration of this specimen with the new method and checks for bias by comparing the
Whomdo you trust? Companies often place advertisements to improve the image of their brand rather than to promote specific products. In a randomized comparative experiment, business students read ads that cited either theWall Street Journal or the National Enquirer for important facts about a
Looking back on love. Choose 40 romantically attached couples in their midtwenties. Interview the man and woman separately about a romantic attachment they had at age 15 or 16. Compare the attitudes of men and women.
Diamonds, continued. Examine the data in Table 17.3 on abundance of carbon-13. Can we use a t confidence interval for mean carbon-13? Explain your answer.Give a 95% confidence interval if you think the result can be trusted.
Diamonds. A group of earth scientists studied the small diamonds found in a nod-CAUTION ule of rock carried up to the earth’s surface in surrounding rock. This is an opportunity to examine a sample from a single population of diamonds formed in a single event deep in the earth.10 Table 17.3 (page
The brain responds, continued. How much more strongly do monkey brains respond to monkey calls than to pure tones? Give a 90% confidence interval to answer this question.
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