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statistical techniques in business

Questions and Answers of Statistical Techniques in Business

Look at Figure 2 at http://ajph.aphapublica tions.org/doi/pdf/10.2105/AJPH.93.4.652, a scatterplot for U.S. states with correlation 0.53 between x = child poverty rate and y = child mortality
The OECD (Organization for Economic Cooperation and Development) consists of advanced, industrialized countries. For these nations, a recent prediction equation6 relating y = child poverty rate to x
Anthropologists often try to reconstruct information using partial human remains at burial sites. For instance, after finding a femur (thighbone), they may want to predict how tall an individual was.
Sketch plots of the following prediction equations, for values of x between 0 and 10:(a) ˆy = 7 + x, (b) ˆy = 7 − x, (c) ˆy = 7, (d) ˆy = x.
For the following variables in a regression analysis, which variable more naturally plays the role of x (explanatory variable) and which plays the role of y (response variable)?(a) College grade
The annual UCLA survey of college freshmen13 indicated that 82% of college freshmen in 2014 considered being financially well-off to be essential or very important, compared to 42% when the survey
Transatlantic Trends is an annual survey of American and European public opinion (http://trends.gmfus.org), with a random sample of about 1000 adults from each of 13 European countries each year. In
The National Health Interview Survey (www.cdc.gov/nchs) estimated that current cigarette smokers were 42% of American adults in 1965 and 20% in 2014.(a) Estimate the difference between the
When a recent Eurobarometer survey asked subjects in each European Union country whether they would be willing to pay more for energy produced from renewable sources than for energy produced from
The National Center for Health Statistics recently estimated that the mean weight for adult American women was 140 pounds in 1962 and 166 pounds in 2010.(a) Suppose these estimates had standard
The U.S. Census Bureau estimated that the median net worth in the United States in 2013 was $142,000 for white households and $11,000 for black households.(a) Identify the response variable and the
In 2013, the U.S. Department of Justice reported that the incarceration rate in the nation’s prisons was 1191 per 100,000 adult male residents (composed of 3% of black males and 0.5% of white
According to the U.S. National Center for Health Statistics, the annual probability that a male between the ages of 20 and 24 is a homicide victim is 0.00164 for blacks and 0.00015 for whites.(a)
TheWorldValues Survey14 asked, “How often do you pray?” The response never was given by 16.5% of the 2232 respondents in the United States and by 44.5% of the 1477 respondents in Australia.(a)
For a random sample of Canadians, 60% indicate approval of the prime minister’s performance. A similar poll a month later has a favorable rating of 57%. A 99%confidence interval for the change in
The College Alcohol Study at the Harvard School of Public Health has interviewed random samples of students at four-year colleges several times since 1993. In the most recent study, of the students
The study mentioned in the previous exercise estimated in 1993 that 19.2% had engaged in unplanned sexual activities because of drinking alcohol; this was 21.3%at the latest survey.(a) Specify
In Great Britain, the Time Use Survey(www.statistics.gov.uk) studied how a random sample of Brits spend their time on a typical day. Of those working full time, 55% of 1219 men and 74% of 733 women
Table 7.14 summarizes responses from General Social Surveys in 1977 and in 2014 to the statement “It is much better for everyone involved if the man is the achiever outside the home and the woman
Refer to the previous exercise. In 2014, of 745 male respondents, 247 (33.2%) agreed. Of 910 female respondents, 268 (29.5%) agreed.(a) Set up notation and specify hypotheses for the hypothesis of no
In a survey conducted by Wright State University, senior high school students were asked if they had ever used marijuana. Table 7.15 shows software output. Treating these observations as a random
A study of compulsive buying behavior (uncontrolled urges to buy) conducted a national telephone survey in 2004 of adults ages 18 and over.15 Of 800 men, 44 were judged to be compulsive buyers
Table 7.16 shows results from the 2014 General Social Survey on belief in an afterlife, classified by sex. Conduct all steps of a significance test, using α = 0.05, to compare the population
A GSS reported that the 486 females had a mean of 8.3 close friends (s = 15.6) and the 354 males had a mean of 8.9 close friends (s = 15.5).(a) A 95% confidence interval for the difference between
Table 7.17 summarizes the number of hours spent in housework per week by gender, based on a recent GSS.(a) Estimate the difference between the population means for women and men.(b) Show that the
A 30-month study evaluated the degree of addiction that teenagers form to nicotine once they begin experimenting with smoking.16 The study used a random sample of 332 seventh-grade students in two
In Great Britain, the Time Use Survey17 studied how a random sample of Brits spend their time on a typical day. For those who reported working full time, Table 7.18 reports the mean and standard
A recent General Social Survey asked, “How many days in the past 7 days have you felt sad?” Software reported sample means of 1.8 for females and 1.4 for males, with a 95% confidence interval
For the 2014 General Social Survey, a comparison of females and males on the number of hours a day that the subject watched TV gave----------------------------------------------Group n Mean StdDev
For the 2014 GSS, Table 7.19 shows software output for evaluating the number of hours of TV watching per day by race.(a) Interpret the reported confidence interval. Can you conclude that one
In a study18 comparing various drink types (alcohol, energy drink, alcohol plus energy, decaffeinated soda) on college students’ desire for additional drinks after various lengths of time, the soda
In a study19 of the effect of the compound tomoxetine as a treatment for adult attention deficit hyperactivity disorder (ADHD), the 21 subjects had an ADHD rating scale mean of 30.0 (s = 6.7) at
As part of her class project, a student at the University of Florida randomly sampled 10 fellow students to investigate their most common social activities. As part of the study, she asked the
Interpret the 95% confidence interval shown.(c) Show how the test statistic shown in the output was obtained from the other information given. Report the P-value, and interpret in context.
Refer to the previous exercise. For comparing parties and sports, software reports a 95% confidence interval of (−3.33, 28.93) and a P-value of 0.106.Explain the connection between the results of
Aclinical psychologist wants to choose between two therapies for treating mental depression. For six patients, she randomly selects three to receive therapy A, and the other three receive therapy B.
Refer to the previous exercise. To avoid bias from the samples being unbalanced with such small n, the psychologist redesigned the experiment. She forms three pairs of subjects, such that the
A study20 of treatments for obesity for rural women examined the impact of a six-month behavioral weight loss program delivered by phone either one-on-one with a counselor or to a group via
For the survey of students described in Exercise 1.11, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for the 51 nonvegetarian students and a mean of 2.22 and
In 2014, the General Social Survey asked about the number of hours a week spent on the World Wide Web, not counting e-mail. The 778 females had a mean of 11.2 and standard deviation of 13.7.The 620
Two new short courses have been proposed for helping students who suffer from severe math phobia, scoring at least 8 on a measure of math phobia that falls between 0 and 10 (based on responses to 10
Recent years have seen impressive improvements in systems for automatically recognizing speech. Research in comparing the quality of different speech recognition systems often uses as a benchmark
A General Social Survey asked subjects their opinions about government spending on health and on law enforcement. Table 7.26 shows results.(a) Find the sample proportion favoring increased spending,
The World Values Survey has asked if homosexuality is justifiable, on a scale from 1 (“never”) to 10 (“always”).In 1981–1984 surveys in the United States of 2325 subjects, 62.4% gave
An experimental study22 of young children’s moral behavior used as subjects 32 three-year-old girls, half assigned to each of two conditions. Each girl and two actors created a picture or clay
In a study about lesbianism, 45 young adults were asked whether they had ever had a same-gender sexual relationship. Table 7.28 shows results. Use software to test whether the probability of this is
For the Students data file (Exercise 1.11 on page 9), use graphical and numerical summaries and inferential statistical methods for the following:(a) Compare political ideology of students
For the data file created in Exercise 1.12, with variables chosen by your instructor, state a research question and conduct inferential statistical analyses. Prepare a report that summarizes your
Using the Comparing Two Means applet at www.artofstat.com/webapps.html, construct two scenarios of independent samples of four men and four women with y = number of hours spent on Internet in past
Exercise 3.6 on page 58 showed data on carbon dioxide emissions, a major contributor to global warming, for advanced industrialized nations. State a research question for these data that involves
Pose null and alternative hypotheses about the relationship between time spent on the Internet (variable WWWHR for the GSS) and a binary explanatory that you believe may be associated with Internet
Browse one or two daily online newspapers such as The New York Times. Find an article about a research study that compared two groups. Prepare a short report that answers the following questions:(a)
A study23 considered whether greater levels of TV watching by teenagers were associated with a greater likelihood of committing aggressive acts over the years. The researchers randomly sampled 707
According to an article in The New York Times (December 6, 2015), the number of annual gun homicides per million people is 31.2 in the United States, 5.6 in Canada, 2.3 in the Netherlands, 0.9 in
The World Values Survey asks if homosexuality is justifiable, on a scale from 1 (“never”) to 10 (“always”).In 1981–1984 surveys, the 2325 respondents in the United States had a mean
The results in Table 7.29 are from a study24 of physical attractiveness and subjective well-being. A sample of college students were rated by a panel on their physical attractiveness. The table
In the World Values Survey, interviews of 1902 subjects in the Netherlands found that 29.2% reported having confidence in the European Union and 33.0% reported having confidence in the government of
In 2011, the United States Supreme Court dealt with a sex discrimination case in which women managers at Walmart earned $14,500 a year less, on the average, than their male counterparts. If you were
The International Adult Literacy Survey25 was a 22-country study in which nationally representative samples of adults were interviewed and tested at home, using the same literacy test having scores
Table 7.30 compares two hospitals on the outcomes of patient admissions for severe pneumonia. Although patient status is an ordinal variable, two researchers who analyze the data treat it as an
From Example 6.4 (page 148), for the cognitive behavioral therapy group the sample mean change in weight of 3.0 pounds was significantly different from 0. However, Example 7.8 (page 194) showed it is
A survey by the Harris Poll of 2250 Americans in 2013 indicated that 42% believe in ghosts, 26% believe in witches, 29% believe in astrology, and 36% believe in creationism.(a) Is it valid to compare
A pool of six candidates for three managerial positions includes three females and three males. Table 7.31 shows the results.(a) Denote the three females by F1, F2, and F3 and the 3 males by M1, M2,
Describe a situation in which it would be more sensible to compare means using dependent samples than independent samples.
An AP story about a University of Chicago survey of 1600 people of ages 15 to 25 in several Midwest U.S.cities indicated that 58% of black youth, 45% of Hispanic youth, and 23% of white youth
True or false? If a 95% confidence interval for(μ2 − μ1) contains only positive numbers, then we can conclude that both μ1 and μ2 are positive.
True or false? If you know the standard error of the sample mean for each of two independent samples, you can figure out the standard error of the difference between the sample means, even if you do
A99% confidence interval for the difference π2−π1 between the proportions of men and women in California who are alcoholics equals (0.02, 0.09).(a) We are 99% confident that the proportion of
To compare the population mean annual incomes for Hispanics (μ1) and for whites (μ2) having jobs in construction, we construct a 95% confidence interval forμ2 − μ1.(a) If the confidence
The Wilcoxon test differs from parametric procedures comparing means in the sense that(a) It applies directly to ordinal as well as interval response variables.(b) It is unnecessary to assume that
A test consists of 100 true–false questions. Joe did not study, so on each question he randomly guesses the correct response.(a) Find the probability that he scores at least 70, thus passing the
Table 8.30 exhibits the maximum possible association between two binary variables for a sample of size n.(a) Show that X2 = n for this table and, hence, that the maximum value of X2 for 2 × 2 tables
For a 2×2 table with cell countsa, b,c, d, the sample log odds ratio logˆθ has approximately a normal sampling distribution with estimated standard errorThe antilogs of the endpoints of the
In an ordinal table, to calculate the number of concordant pairs C, start at the corner of the table for the low level for each variable. Multiply that cell count by the count in every cell that is
A chi-squared variable with degrees of freedom equal to df has representation z21+ · · · + z2 df, where z1, . . . , zdf are independent standard normal variates.(a) If z is a test statistic that
Construct a 3×3 table for which gamma equals (a)1, (b) −1, (c) 0.
For 2×2 tables, gamma simplifies to a measure first proposed about 1900 by the British statistician G. Udny Yule, who also introduced the odds ratio. In that special case, gamma is called Yule’s
Each subject in a sample of 100 men and 100 women is asked to indicate which of the following factors (one or more) are responsible for increases in crime committed by teenagers: A—the increasing
The correct answer in Exercise 8.38(c) implies that if the chi-squared statistic is used for a contingency table having ordered categories in both directions, then (select the correct response(s))(a)
Answer true or false for the following. Explain your answer.(a) Even when the sample conditional distributions in a contingency table are only slightly different, when the sample size is very large
(a) When the sample size is very large, we have not necessarily established an important result when we show a statistically significant association. Explain.(b) The remarks in Sections 8.3 and 8.4
Shortly before a gubernatorial election, a poll asks a random sample of 50 potential voters the following questions:Party: Do you consider yourself to be a Democrat (D), a Republican (R), or an
An abstract of an article6 dealing with alcohol use and sexual assault among college women stated,“This study prospectively examined the relation between alcohol use and sexual assault in a sample
For 2014 GSS data, of those identifying as Democrats, 496 classified themselves as liberal and 171 as conservative. Of those identifying as Republicans, 56 called themselves liberal and 499
Does belief in evolution vary according to religious beliefs? Examine this using Table 8.28, for respondents to the 2014 General Social Survey. The variables are Fundamentalism/Liberalism of
Pose a research question about attitude regarding homosexual relations and political ideology. Using the most recent GSS data on variables HOMOSEX and POLVIEWS, conduct a descriptive and inferential
One year the GSS asked how housework was shared between the respondent and his or her spouse. Possible responses were 1 = I do much more than my fair share, 2 =I do a bit more than my fair share, 3 =
Refer to the data file you created in Exercise 1.12.For variables chosen by your instructor, pose a research question and conduct descriptive and inferential statistical analyses. Interpret and
Refer to the Students data file (Exercise 1.11 on page 9). Using software, create and analyze descriptively and inferentially the contingency table relating opinion about abortion and (a) political
Refer to Exercise 8.13 on happiness and income.The analysis there does not take into account the ordinality of the variables. Using software, summarize the strength of association by finding and
A GSS cross-classified income in thousands of dollars(25) by job satisfaction (very dissatisfied, a little satisfied, moderately satisfied, very satisfied)for black Americans. Software provides the
For the 2014 GSS, γˆ = 0.19 for the relationship between job satisfaction (categories very dissatisfied, little dissatisfied, moderately satisfied, very satisfied) and family income (below average,
Table 8.25 cross-classifies happiness with family income for the subsample of the 2014 GSS that identified themselves as Jewish.(a) Give an example of a (i) concordant pair, (ii) discordant pair.(b)
According to a 2015 study by the Pew Research Center (www.people-press.org), the percentage of Americans who favor allowing gays and lesbians to marry legally was 81% for Democrats who identified
Refer to Table 8.1 (page 216) on political party ID and gender. Find and interpret the odds ratio for each 2×2 subtable. Explain why this analysis suggests that the last two columns show a very weak
According to the U.S. Bureau of Justice Statistics, in 2014 the incarceration rate in the nation’s prisons was 904 per 100,000 male residents, 65 per 100,000 female residents, 2805 per 100,000
The 2012 National Survey on Drug Use and Health(NSDUH) estimated that 23% of Americans aged 12 or over reported binge drinking in the past month, and 7%had used marijuana in the past month.(a) Find
Table 8.24 cross-classifies 68,694 passengers in autos and light trucks involved in accidents in the state of Maine by whether they were wearing a seat belt and by whether they were injured or
In a survey of senior high school students inDayton, Ohio, 1449 students had used both alcohol and cigarettes, 281 had used neither, 500 had used alcohol but not cigarettes, and 46 had used
In a recent GSS, the death penalty for subjects convicted of murder was favored by 74% of whites and 43%of blacks. It was favored by 75% of males and 63% of females.In this sample, which variable was

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