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Statistics Informed Decisions Using Data 5th Edition Michael Sullivan III - Solutions
Stock fund managers are investment professionals who decide which stocks should be part of a portfolio. In a recent article in the Wall Street Journal (Not a Stock-Picker's Market, WSJ January 25, 2014), the performance of stock fund managers was considered based on dispersion in the market. In the
Why do we use a pooled estimate of the population proportion when testing a hypothesis about two proportions? Why do we not use a pooled estimate of the population proportion when constructing a confidence interval for the difference of two proportions?
A researcher wishes to determine the effects of alcohol on people's reaction time to a stimulus. She randomly divides 100 people aged 21 or older into two groups. Group 1 is asked to drink 3 ounces of alcohol, while group 2 drinks a placebo. Both drinks taste the same, so the individuals in the
The Gallup Organization asked 1050 randomly selected adult Americans age 18 or older who consider themselves to be religious, "Do you believe it is morally acceptable or morally wrong [rotated] to conduct medical research using stem cells obtained from human embryos?" The same question was asked to
A political scientist wants to know how a random sample of 18- to 25-year-olds feel about Democrats and Republicans in Congress. She obtains a random sample of 1030 registered voters 18 to 25 years of age and asks, "Do you have favorable/ unfavorable [rotated] opinion of the Democratic/Republican
In a Gallup poll 513 national adults aged 18 years or older who consider themselves to be Republican were asked, "Of every tax dollar that goes to the federal government in Washington, D.C., how many cents of each dollar would you say are wasted?" The mean wasted was found to be 54 cents with a
Stocks may be categorized by sectors. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_3_17 using the file format of your choice for the version of the text you are using. The data represent the one-year rate of return (in percent) for a sample of consumer cyclical stocks and
Do women feel differently from men when it comes to federal tax rates? One question on the Sullivan Statistics Survey II was, "What percent of income do you believe individuals should pay in federal income tax?" Results of the survey may be found at www.pearsonhighered.com/sullivanstats. Select the
PayScale is a company that reports statistics on colleges and universities. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_3_24 using the file format of your choice for the version of the text you are using. The data contain the four-year cost and graduation rate for over
The Collegiate Learning Assessment Plus (CLA+) is an exam that is meant to assess the intellectual gains made between one's freshman and senior year of college. The exam, graded on a scale of 400 to 1600, assesses critical thinking, analytical reasoning, document literacy, writing, and
In a MythBusters episode, the question was asked, "Which is better? A four-way stop or a roundabout?" "Better" was determined based on determining the number of vehicles that travel through the four-way stop over a 5-minute interval of time. Suppose the folks at MythBusters conducted this
It has been reported that consumption of sodas and other sugar-sweetened beverages cause excessive weight gain. Researchers conducted a randomized study in which 224 overweight and obese adolescents who regularly consumed sugar-sweetened beverages were randomly assigned to experimental and control
Researcher Seth B. Young measured the walking speed of travelers in San Francisco International Airport and Cleveland Hopkins International Airport. The standard deviation speed of the 35 travelers who were departing was 53 feet per minute. The standard deviation speed of the 35 travelers who were
Lowbirth weight babies are at increased risk of respiratory infections in the first few months of life and have low liver stores of vitamin A. In a randomized, double-blind experiment, 130 lowbirth weight babies were randomly divided into two groups.Subjects in group 1 (the treatment group, n1 =
A researcher wants to know if students who do not plan to apply for financial aid had more variability on the SAT I math test than those who plan to do so. She obtains a random sample of 35 students who do not plan to apply for financial aid and a random sample of 38 students who do plan to apply
McDonald's executives want to experiment with redesigning its restaurants so that the customers form one line leading to four registers to place orders, rather than four lines leading to four separate registers. They redesign 30 randomly selected restaurants with the single line. In addition, they
A quality-control engineer wants to find out whether or not a new machine that fills bottles with liquid has less variability than the machine currently in use. The engineer calibrates each machine to fill bottles with 16 ounces of a liquid. After running each machine for 5 hours, she randomly
Stocks may be categorized by sectors. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 11_4_21 using the file format of your choice for the version of the text you are using. The data represent the one-year rate of return (in percent) for a sample of consumer cyclical stocks and
Researchers at the University of Mississippi wanted to discover whether variability for reaction time to a go/no go stimulus of males was different from that of females. The researchers randomly selected 20 females and 15 males to participate in the study. The go/no go stimulus required the student
Two-tailed test with a = 0.05, degrees of freedom in the numerator = 6, degrees of freedom in the denominator = 8.Find the critical value(s) for a:
Two-tailed test with α = 0.02, degrees of freedom in the numerator = 5, degrees of freedom in the denominator = 7.Find the critical value(s) for α:
Left-tailed test with α = 0.10, degrees of freedom in the numerator = 25, degrees of freedom in the denominator = 20. Find the critical value(s) for α:
Left-tailed test with α = 0.01, degrees of freedom in the numerator = 15, degrees of freedom in the denominator = 20. Find the critical value(s) for a:
Right-tailed test with α = 0.05, degrees of freedom in the numerator = 45, degrees of freedom in the denominator = 15. Find the critical value(s) for α:
Right-tailed test with α = 0.01, degrees of freedom in the numerator = 55, degrees of freedom in the denominator = 50. Find the critical value(s) for α
Assume that the populations are normally distributed. Test the given hypothesis.σ1 ≠σ2 at the α = 0.05 level of significance
What is the typical age difference between husband and wife? The following data represent the ages of husbands and wives, based on results from the Current Population Survey.(a) What is the response variable in this study?(b) Is the sampling method dependent or independent? Explain.(c) Use the data
The average major league fastball is 92.0 miles per hour (mph). While there are many other factors other than velocity that are used to judge the quality of this pitch (location and movement, for example), velocity is a major factor in deciding whether a pitcher has "big league stuff." Suppose a
Do wet suits allow a swimmer to swim faster? Researchers measured the speed (in meters per second) of swimmers both with and without a wetsuit. The results of the study are shown in the table. Conduct the appropriate test to determine whether the data suggest that wet suits allow a swimmer to swim
Is there a difference in the attitude toward extramarital affairs in the United States versus Canada? Pew Research surveyed a random sample of adults from each country and asked, "Do you personally believe that married people having an affair is morally acceptable?" Results of the surveys are
In today's "wired" society, students believe that they can multitask. Research suggests that 5% of individuals truly have the ability to multitask. Can students multitask, or do they perform worse while multitasking? In an introductory accounting class, students were randomly given an instruction
If n1 = 31, s1 = 12, n2 = 51, and s2 = 10, test whether σ1 > σ2 at the α = 0.05 level of significance.
The following data represent the 5-year rate of return (in percent) for a random sample of stocks in financial services and an independent random sample of stocks in health care(a) Has there been a difference in the rate of return of companies in the Financial Services sector versus those in the
As of October 1, 2012, hospitals in the United States with excessive numbers of readmissions based on the Centers for Medicare and Medicaid Services (CMS) data were penalized. Therefore, it is important for hospitals to identify the risk factors associated with readmission. The following data
Researchers wanted to determine whether individuals considered certain employee work behaviors to be required or optional. For each work behavior cited, participants rated the behavior on a scale from 1 (definitely required) to 7 (completely optional). There were a total of 41 individuals who rated
It has long been a concern that there is a wage gap between men and women in the United States with some reports suggesting that women only make $0.77 for every dollar earned by a man. Design a study that would allow you to confirm whether a wage gap does actually exist.
If n1 = 61, s1 = 18.3, n2 = 57, and s2 = 13.5, test whether the population standard deviations differ at the α = 0.05 level of significance.Perform the appropriate hypothesis test.
Using the data from Problem 9, test whether the standard deviation of wait time at Wendy's is more than that at McDonald's at the a = 0.05 level of significance.
Height versus Arm Span Construct and interpret a 95% confidence interval for the population mean difference between height and arm span using the data from Problem 8. What does the interval lead us to conclude regarding any differences between height and arm span?
McDonald's versus Wendy's Construct and interpret a 95% confidence interval about µM - µW using the data from Problem 9. How might a marketing executive with McDonald's use this information?
(a) Find the critical F-value for a right-tailed test with a = 0.05, degrees of freedom in the numerator = 8, and degrees of freedom in the denominator = 9.(b) Find the critical F-value for a two-tailed test with a = 0.05, degrees of freedom in the numerator = 10, and degrees of freedom in the
According to the manufacturer of M&Ms, 13% of the plain M&Ms in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of plain M&Ms. He counted the number of M&Ms that were each color and obtained the results shown in the
According to the manufacturer of M&Ms, 12% of the peanut M&Ms in a bag should be brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green. A student randomly selected a bag of peanut M&Ms. He counted the number of M&Ms that were each color and obtained the results shown in
Our number system consists of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9 because we do not write numbers such as 12 as 012. Although we may think that each first digit appears with equal frequency so that each digit
Refer to Problem 13. The distribution in the next column lists the first digit of the surface area (in square miles) of 335 rivers. Is there evidence at the α = 0.05 level of significance to support the belief that the distribution follows Benford's Law?
The National Highway Traffic Safety Administration publishes reports about motorcycle fatalities and helmet use. The distribution shows the proportion of fatalities by location of injury for motorcycle accidents.The following data show the location of injury and number of fatalities for 2068 riders
Is the religious make-up of the United States Congress reflective of that in the general population? The following table shows the religious affiliation of the 535 members of the 114th Congress along with the religious affiliation of a random sample of 1200 adult Americans.(a) Determine the
Does the location of your seat in a classroom play a role in attendance or grade? To answer this question, professors randomly assigned 400 students* in a general education physics course to one of four groups. The 100 students in group 1 sat 0 to 4 meters from the front of the class, the 100
On January 1, 2004, it became mandatory for all police departments in Illinois to record data pertaining to race from every traffic stop. Mundelein, Illinois, has been collecting data since 2000. Rather than using census data to determine the racial distribution of the village, they thought it
In his book Outliers, Malcolm Gladwell claims that more hockey players are born in January through March than in October through December. The following data show the number of players in the National Hockey League in the 2014-2015 season according to their birth month. Is there evidence to suggest
A researcher wanted to determine whether bicycle deaths were uniformly distributed over the days of the week. She randomly selected 200 deaths that involved a bicycle, recorded the day of the week on which the death occurred, and obtained the following results (the data are based on information
A researcher wanted to determine whether pedestrian deaths were uniformly distributed over the days of the week. She randomly selected 300 pedestrian deaths, recorded the day of the week on which the death occurred, and obtained the following results (the data are based on information obtained from
A player in a craps game suspects that one of the dice is loaded. A loaded die is one in which all the possibilities (1, 2, 3, 4, 5, and 6) are not equally likely. The player throws the die 400 times, records the outcome after each throw, and obtains the following results:(a) Do you think that the
An urban economist wonders if the distribution of U.S. residents in the United States is different today than it was in 2000. The table shows the distribution of residents in 2000 along with the observed counts of residents today based on a random sample of 1500 US residents.(a) Does the sample
According to the U.S. Census Bureau, 7.1% of all babies born are of low birth weight (<5 lb, 8 oz). An obstetrician wanted to know whether mothers between the ages of 35 and 39 years give birth to a higher percentage of low-birth-weight babies. She randomly selected 240 births for which the
In 2000, 25.8% of Americans 15 years of age or older lived alone, according to the Census Bureau. A sociologist, who believes that this percentage is greater today, conducts a random sample of 400 Americans 15 years of age or older and finds that 164 are living alone.(a) If the proportion of
In Thomas Pynchon's book Gravity Rainbow, the characters discuss whether the Poisson probabilistic model can be used to describe the locations that Germany's feared V-2 rocket would land in. They divided London into 0.25-km2 regions. They then counted the number of rockets that landed in each
On February 2, 1894, Frank Raphael Weldon wrote a letter to Francis Galton that included the results of 26,306 rolls of 12 dice. Weldon recorded the results such that a roll of a 5 or 6 resulted in a success, while a roll of 1, 2, 3, or 4 was a failure. The number of successes in each roll of the
How much does the typical person pay for a new 2015 Buick Regal? The following data represent the selling price of a random sample of new Regals (in dollars).(a) Is this data quantitative or qualitative? (b) Find the mean and median price of a new 2015 Regal. (c) Find the standard deviation and
Why is goodness of fit a good choice for the title of the procedures used in this section?
If the expected count of a category is less than 1, what can be done to the categories so that a goodness-of-fit test can still be performed?
Determine the expected counts for each outcome.
Determine (a) the x2 test statistic, (b) the degrees of freedom, (c) the critical value using a = 0.05, and (d) test the hypothesis at the a = 0.05 level of significance.H0: pA = pB = pC = pD = 1/4H1: At least one of the proportions is different from the others.
Does amount of education play a role in the healthiness of an individual? The following data represent the level of health and the highest degree earned for a random sample of individuals from the General Social Survey.(a) Does the evidence suggest that health and education are related? Use the
The Gallup Organization conducted a survey in 2014 asking individuals questions pertaining to social well-being such as strength of relationship with spouse, partner, or closest friend, making time for trips or vacations, and having someone who encourages them to be healthy. Social well-being
The following data represent the smoking status from a random sample of 1054 U.S. residents 18 years or older by level of education.(a) Test whether smoking status and level of education are independent at the α = 0.05 level of significance.(b) Construct a conditional distribution of smoking
Do electronic cigarettes assist in helping individuals quit smoking? Researchers found 300 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of
Celebrex, a drug manufactured by Pfizer, Inc., is used to relieve symptoms associated with osteoarthritis and rheumatoid arthritis in adults. In clinical trials of the medication, some subjects reported dizziness as a side effect. The researchers wanted to discover whether the proportion of
In a recent survey conducted by the Pew Research Center, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word socialism. In addition, the individuals were asked to disclose which political party they most associate with.
In a recent survey conducted by the Pew Research Center, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word capitalism. In addition, the individuals were asked to disclose which political party they most associate with.
A survey was conducted at a community college of 50 randomly selected students who dropped a course in the current semester to learn why students drop courses. "Personal" drop reasons include financial, transportation, family issues, health issues, and lack of child care. "Course" drop reasons
Traditional underwriting to determine the risks associated with lending include credit scores, income, and employment history. The online lender ZestFinance used data analysis to find that people who fill out loan applications using all capital letters default more often than those who use all
A study by InsuranceQuotes.com found that homeowners with poor credit pay 91% more for home insurance than people with excellent credit. (a) A quote in the article stated, "Insurers have found a direct correlation between a consumer's credit and the likelihood that he or she will make a home (or
In a famous study by the Physicians Health Study Group from Harvard University from the late 1980s, 22,000 healthy male physicians were randomly divided into two groups; half the physicians took aspirin every other day, and the others were given a placebo. Of the physicians in the aspirin group,
(a) Draw a relative frequency histogram of the distance a homerun traveled in 2014 using a lower class limit of the first class of 300 and a class width of 10. Describe the shape of the distribution.(b) Find the population mean and population standard deviation distance.(c) Find the quartiles of
Explain the differences between the chi-square test for independence and the chi-square test for homogeneity. What are the similarities?
The following table contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories:(a) Compute the value of the chi-square test statistic.(b) Test the hypothesis that X and Y are independent
The table in the next column contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories.(a) Compute the value of the chi-square test statistic.(b) Test the hypothesis that X and Y are
The following table contains the number of successes and failures for three categories of a variable.Test whether the proportions are equal for each category at the a = 0.01 level of significance.
The following table contains the number of successes and failures for three categories of a variable.Test whether the proportions are equal for each category at the α = 0.01 level of significance.
A sociologist wants to discover whether the sexual activity of females between the ages of 15 and 19 years and family structure are associated. She randomly selects 380 females between the ages of 15 and 19 years and asks each to disclose her family structure at age 14 and whether she has had
An obstetrician wants to learn whether the amount of prenatal care and the wantedness of the pregnancy are associated. He randomly selects 939 women who had recently given birth and asks them to disclose whether their pregnancy was intended, unintended, or mistimed. In addition, they were to
Are health and happiness related? The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey.(a) Does the evidence suggest that health and happiness are related? Use the α = 0.05 level of significance.(b) Construct a
The General Social Survey asked a random sample of adult Americans two questions: (1) Would you favor or oppose a law which would require a person to obtain a police permit before he or she could buy a gun? (2) Do you favor or oppose the death penalty for persons convicted of murder? Results of the
The General Social Survey asked a random sample of adult Americans with children two questions: (1) Do you believe there should be paid leave for childcare? (2) Do you believe children are a financial burden on parents? Results of the survey are in the following table. Does the sample evidence
A pit boss suspects that a roulette wheel is out of balance. A roulette wheel has 18 black slots, 18 red slots, and 2 green slots. The pit boss spins the wheel 500 times and records the following frequencies:Outcome _________________ FrequencyBlack .................................233Red
Are the teams that play in the World Series evenly matched? To win a World Series, a team must win four games. If the teams are evenly matched, we would expect the number of games played in the World Series to follow the distribution shown in the first two columns of the following table. The third
With 20% of men, 74% of women, and 52% of children surviving the infamous Titanic disaster, it is clear that the saying "women and children first" was followed. But what, if any, role did the class of service play in the survival of passengers? The data shown represent the survival status of
Does the length of term of pregnancy play a role in the level of education of the baby? Researchers in Norway followed over 1 million births between 1967 and 1988 and looked at the educational attainment of the children. The following data are based on the results of their research. Note that a
One of the most famous presidential elections (from a statistician's point of view) is the 1936 contest between incumbent Franklin D. Roosevelt (FDR) and Republican challenger Alf Landon. The notoriety of the election comes from the fact that polling done by Literary Digest suggested that Landon
In the General Social Survey, individuals were asked whether civic duty included voting and whether it included serving on a jury. The results of the survey are shown in the table. Is there a difference in the proportion of individuals who feel jury duty is a civic duty and the proportion of
The following data represent a simple random sample of n = 4 from three populations that are known to be normally distributed. Verify that the F-test statistic is 2.04.
The following data represent a simple random sample of n = 5 from three populations that are known to be normally distributed. Verify that the F-test statistic is 2.599.
The data in the table represent the number of corn plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plot. An agricultural researcher wants to know whether the mean number of plants for each plot type are equal.(a) Write the null and alternative hypotheses.(b) State
The data in the table represent the number of pods on a random sample of soybean plants for various plot types. An agricultural researcher wants to determine if the mean numbers of pods for each plot type are equal.(a) Write the null and alternative hypotheses.(b) State the requirements that must
At a community college, the mathematics department has been experimenting with four different delivery mechanisms for content in their Intermediate Algebra courses. One method is the traditional lecture (method I), the second is a hybrid format in which half the class time is online and the other
An obstetrician knew that there were more live births during the week than on weekends. She wanted to determine whether the mean number of births was the same for each of the five days of the week. She randomly selected eight dates for each of the five days of the week and obtained the following
A stock analyst wondered whether the mean rate of return of financial, energy, and utility stocks differed over the past five years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the five-year rates of return shown in the following table (in
In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three groups: Group 1, the simple group, required to respond as quickly as possible after a stimulus was
To determine if there is gender and/or race discrimination in car buying, Ian Ayres put together a team of fifteen white males, five white females, four black males, and seven black females who were each asked to obtain an initial offer price from the dealer on a certain model car. The 31
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