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mathematics
introduction to business statistics
Introduction To Statistical Investigations 1st Edition Beth L.Chance, George W.Cobb, Allan J.Rossman Nathan Tintle, Todd Swanson Soma Roy - Solutions
The table below shows the numbers of male and female rattlesnakes caught at two different sites, B and G. Assume that the snakes caught at a site can be regarded as a random sample from the population of all snakes at the site.We want to know whether there is an association between site and sex.
The U.S. government authorizes private contractors to audit bills paid by Medicare and Medicaid. The contractor audits a random sample of paid claims and judges each claim to be either fully justified or an over payment. Here is a 2 × 2 table that summarizes data from one such audit.
Think about the proportion of students at your college who are wearing clothing that displays the college name or logo today. Also suppose that a friend of yours attends a different college, and the two of you have a recurring discussion about which college displays more school pride. You decide to
Fill in the cells in the following table so there is no association between the explanatory and response variables. Member of Fraternity or Sorority Yes No Total Yes 152 Has one or more alcoholic drinks per week No 230 Total 42 340 382
Fill in the cells in the following table so there is no association between the explanatory and response variables. Female Total Male Played sports in high school Yes 200 160 No Total 150 210 360
Consider the following two 2 × 2 tables:a. Calculate the proportion of failures for all four treatments.b. Calculate the difference in proportions of failure between Treatments A and B. Then do the same calculation to compare Treatments C and D.c. Calculate the relative risk of failure
Four 2 × 2 tables, numbered 1€“4, are shown below. For each one the response is Yes/No and the explanatory variable is A/B.a. Which two tables have the same pair of conditional proportions?b. For which table(s) is the difference (A versus B) in conditional proportions the
Causation. Is a cause-effect conclusion possible in this new study? Why or why not?
Generalization. Have the researchers addressed the concerns about generalization with this new study?
Write a conclusion about the strength of evidence in this new study based on obtaining a p-value of 0.024.
In this study, what proportion of those on the suspension bridge called the interviewer? Of those who had already crossed the bridge?Let’s see how this second study turned out. Of those on the suspension bridge, 13 of the 20 men called the female interviewer. Of those that had already crossed the
Describe the confounding variable they are trying to eliminate by completing this new study.The researchers acknowledged the fact that there were confounding variables involved in this study. They tried to minimize these by doing other studies to try to answer the same research question. In another
Causation. What about cause-and-effect conclusions? Did the researchers use random assignment to determine which of the 34 men crossed the suspension bridge and which crossed the wooden bridge? Are we able to conclude that the cause of the difference between the two groups of men was the type of
Generalization. Now, let’s step back a bit and think about the scope of our inference. Was this a random sample? Does this study represent all people? How about all men? Is there any population to which we can generalize our conclusion?In Chapter 5, we will learn how to use the 3S strategy to
In studies comparing two groups, the parameter of interest is oft en stated as the true difference in the long-run proportions in the two groups. In this study, this is the long run difference in the proportions of men calling the researcher comparing the men crossing the Capilano suspension bridge
Write a conclusion about the strength of evidence in the study based on the p-value from #8.In Chapter 5, we will learn how to use the 3S strategy to help us investigate how much evidence the sample data provide to support our conjecture that the long-run probability of men who call is greater for
Use the null and alternative hypotheses stated above and the p-value of 0.023 to write a conclusion about strength of evidence in this study. (Hint: Even though the study design is different, the way you interpret p-values in terms of the null and alternative hypothesis is still the same.)
What proportion of men on the wooden bridge called the interviewer?Social psychologists throughout the years have shown that an aggression-sexuality link exists not only in various animal species but also in humans. Dutton and Aron (Journal of Personality and Social Psychology, 1974) set out to
What proportion of men on the suspension bridge called the interviewer?
We have two variables: bridge type and whether the subject called or not. Which of these variables is explanatory and which is response?
Fill in the two-way table with the data from the study. Wooden bridge Suspension bridge Totals Subject called interviewer 11 Subject did not call interviewer 23 Totals 34 18 16
What are the observational units?The researcher is now interested in seeing whether a higher proportion of men in the group that crossed the Capilano Canyon bridge will call her versus the proportion of calls she will receive from the group that crossed the solid wooden bridge.
Is this an observational study or an experiment? How are you deciding?The researcher is now interested in seeing whether a higher proportion of men in the group that crossed the Capilano Canyon bridge will call her versus the proportion of calls she will receive from the group that crossed the
Are people who attend church regularly less likely to smoke than people who do not attend church regularly? Is it possible to design a randomized experiment to investigate this question? If so, describe how you would design such an experiment. If not, explain why not.
Are American adults who have children significantly more likely to play video games than American adults who do not have children? Is it possible to design a randomized experiment to investigate this question? If so, describe how you would design such an experiment. If not, explain why not.
Do college professors who use a red pen to grade student essays tend to assign lower scores, on average, than professors who use a blue pen to grade student essays? Describe how you could design a randomized experiment to investigate this question.
Do restaurant customers tend to order more expensive meals when classical music is playing in the background than when other kinds of music are playing in the background? Describe how you could design a randomized experiment to investigate this question.
You want to investigate whether teenagers in the United Kingdom (UK) tend to have read more Harry Potter books, on average, than teenagers in the United States (US).a. Identify and classify (as categorical or quantitative) the explanatory and response variable.b. Would you ideally use random
Studies have shown that children in the U.S. who have been spanked have a significantly lower IQ score on average than children who have not been spanked.a. Is it legitimate to conclude from this study that spanking a child causes a lower IQ score? Explain why or why not.b. Explain why conducting a
Ian Ayres, the author of a popular book titled Super Crunchers, conducted a study to help him decide what to name his book. He placed an ad on google.com, with the ad sometimes giving the title as Super Crunchers and other times giving the title as Th e End of Intuition. Google provided Ayres with
A study found that college students who live off - campus are significantly more likely to drink alcohol than those who live on-campus.a. Do you suspect that this was an observational study or an experiment? Explain.b. Is it appropriate to conclude that living off -campus causes a student to be
A poll conducted by the Gallup organization asked American adults whether or not they are generally satisfied with their physical attractiveness. One goal of the study was to investigate whether men and women diff er with regard to responses on this issue.a. Identify the explanatory and response
An article in a 2006 issue of Journal of Behavioral Decision Making reports on a study involving 47 undergraduate students in a class at Harvard. All of the participants were given $50, but some (chosen at random) were told that this was a “tuition rebate,” while the others were told that this
Is random sampling or random assignment the more important consideration if the research question is whether faculty tend to drive older cars than students drive on your campus?
Which of the following is true of experiments?A. The researchers assign the explanatory variable to subjects.B. The researchers assign the response variable to subjects.C. The researchers assign both the explanatory and response variables to subjects.D. The researchers assign neither the
In August 1998, an article titled “Prayer Can Lower Blood Pressure” appeared in the USA Today. The article was based on the findings of a study by the National Institutes of Health Initiatives that followed 2,391 people aged 65 years or more. The article said: “People who attended a religious
Enamored with the solitaire game on his new computer, Author A sets out to estimate his probability of winning the game and wins 25 games while losing 192 games. Anxious to outperform Author A, Author B plays 444 games of solitaire and wins 74. Author B wants to know if they are performing
Recall the data from the STAR study: Of the 9,726 women randomly assigned to use tamoxifen daily, 163 developed invasive breast cancer sometime during the next five years, compared to 168 in the group of 9,745 who were randomly assigned to use raloxifene daily.a. Calculate the observed value of the
Recall the data from the STAR study: Of the 9,726 women randomly assigned to use tamoxifen daily, 163 developed invasive breast cancer sometime during the next five years, compared to 168 in the group of 9,745 who were randomly assigned to use raloxifene daily.a. Define the parameters of interest.
Researchers Vogel et al. (JAMA, 2006) reported the following findings about the Study of Tamoxifen and Raloxifene (STAR), a study involving postmenopausal women who were at an increased risk for invasive breast cancer. Of the 9,726 women randomly assigned to use tamoxifen daily, 163 developed
Recall exercise 5.2.29 about the use of incentives to encourage people to participate in a telephone survey. A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on telephone surveys. A national sample
Reconsider a previous exercise from Section 5.1 about Medicare audits. Of the 30 small claims, 14 were judged to be overpayments; of the 30 medium claims, 8 were judged to be overpayments. Our research question is this: “Does the chance that the claim is judged to be an overpayment tend to diff
Reconsider the previous exercise. If a 99% confidence interval had instead been produced from the same sample data for the parameter π05-06 − π88-94, what would the width of this confidence interval be? If the width can be calculated, find it. If the width cannot be calculated using only the
Reconsider the previous exercise. If a 99% confidence interval had instead been produced from the same sample data for the parameter π05-06 − π88-94, what would the midpoint of this confidence interval be? If the midpoint can be calculated, find it. If the midpoint cannot be calculated using
Reconsider the previous exercise. If a 99% confidence interval had instead been produced from the same sample data for the parameter π05-06 − π88-94, how would this confidence interval have turned out?A. Wider than the 95% confidence interval: (0.0015, 0.0467)B. Narrower than the 95% confidence
Reconsider the previous exercise. If a 95% confidence interval had instead been produced from the same sample data for the parameter π88-94 − π05-06, how would this confidence interval have turned out?A. Same as above: (0.0015, 0.0467)B. Negative of above: (−0.0467, −0.0015)C. Impossible to
Researchers investigated whether the proportion of American teenagers with some level of hearing loss was different in 2005–2006 than in 1988–1994. They collected data on random samples of American teenagers in those two time periods. Let the symbol π05-06 denote the population proportion of
Read FAQ 5.2.2 about randomness and answer the following questions.a. Suppose we get a small p-value in an observational study comparing two proportions with no random assignment. What can we rule out as an explanation for the difference in proportions? Can we conclude there is a cause? Can we
Read FAQ 5.2.1 about comparing the statistics difference in proportions and relative risk. In the dolphin therapy study mentioned in that FAQ there were 15 people assigned to swim with dolphins and 15 who were not (the control). We also saw that 13 people showed improvement of their depression
Reconsider the study about the effects of “romantic lyrics on compliance with a courtship request.” Recall that of the 44 women who listened to the romantic song, 23 gave their phone numbers, whereas of the 43 who listened to the neutral song, only 12 did.a. Use an appropriate
Reconsider the data from the previous study about the effects of “romantic lyrics on compliance with a courtship request.”a. Define (in words) the parameters of interest of this study. Also, assign symbols to the parameters.b. State the null and alternative hypotheses in words.c. State the null
In an article published in Psychology of Music (2010), researchers reported the results of a study conducted to investigate the effects of “romantic lyrics on compliance with a courtship request.” Th e researchers recruited undergraduate female students who were studying social and managerial
Reconsider the data from Singer et al.’s study about whether incentives improve response rates on telephone surveys.a. Use an appropriate randomization-based applet to find a p-value. Report and interpret the p-value in the context of the study.b. Based on this p-value, how much evidence do you
Reconsider the data from Singer et al.’s study about whether incentives improve response rates on telephone surveys.a. State the null and alternative hypotheses in words.b. State the null and alternative hypotheses in symbols.c. Give detailed, step-by-step instructions on how one could conduct a
A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on telephone surveys. A national sample of 735 households was randomly selected, and all 735 of the households were sent an “advance letter”
Recall the previous exercise, which described the Italian firm Ma-Vib that was in the news for €œsexual discrimination€ for having chosen only its female employees to be dismissed. Before the layoff s, Ma-Vib employed 18 women and 12 men; it then fi red 15 of the women and none
In July 2011, an Italian firm Ma-Vib was in the news for “sexual discrimination” for having chosen only its female employees to be dismissed. Before the layoff s, Ma-Vib employed 18 women and 12 men; it then fired 15 of the women and none of the men.a. What proportion of the men were fired?b.
Have you ever donated blood? If so, how often do you donate blood? Studies have looked at who is more likely to donate blood: men or women? Suppose that three students, Eddie, Francisco, and Gina, each decide to take random samples of men and women and ask each of the participants whether they have
Suppose that three high school students separately conduct polls in their city to investigate if there is an association between being a vegetarian and whether people like to eat at home or eat at restaurants.• Sally finds that 35 out of 45 vegetarians preferred to eat at home whereas 20 out of
Reconsider the data from Th e Pew Research Center for the People survey of U.S. adults to investigate whether there is an association between a person’s level of education and her/his awareness of her/his response to the Census being required by law.a. Use an appropriate randomization-based
Reconsider the data from The Pew Research Center for the People survey of U.S. adults to investigate whether there is an association between a person’s level of education and her/his awareness of her/his response to the Census being required by law.a. State the appropriate null and alternative
A survey of a random sample of U.S. adults by The pew Research Center for the People and the Press conducted in early January 2010 recorded each participant’s highest level of education completed and whether they knew that responding to the Census was required by law. Of the 973 participants who
Reconsider the data from the 2013 Gallup poll that asked randomly selected U.S. adults whether they wanted to stay at their current body weight or change.a. Use an appropriate randomization-based applet to find a p-value. Report and interpret the p-value in the context of the study.b. Based on this
Reconsider the data from the 2013 Gallup poll that asked randomly selected U.S. adults whether they wanted to stay at their current body weight or change.a. State the appropriate null and alternative hypotheses in words.b. State the appropriate null and alternative hypotheses in symbols. Be sure to
A 2013 Gallup poll asked randomly selected U.S. adults whether they wanted to stay at their current body weight or change. One purpose was to investigate whether there was any difference between men and women with regard to this aspect. Of the 562 men surveyed, 242 wanted to stay at their current
Reconsider the data from the study investigating whether people who hold high-power poses are more likely to take risks (such as the double or nothing bet) compared to those who hold low-power poses.a. Calculate the observed value of the relative risk of taking the bet for those who held high-power
Reconsider the data from the study investigating whether people who hold “high-power poses” are more likely to take risks (such as the double or nothing bet) compared to those who hold “low-power poses.” For this exercise, for a statistic use the difference in the conditional proportion of
Reconsider the data from the study investigating whether people who hold high-power poses are more likely to take risks (such as the double or nothing bet) compared to those who hold low-power poses. For this exercise, use the difference in the conditional proportion of bet takers between those who
In the Chapter 4 exercises you read about a research article, €œPower Posing: Brief Nonverbal Displays Affect Neuroendocrine Levels and Risk Tolerance,€ that was published in Psychological Science, September 2010, and describes an experiment involving 42 participants (male and
Reconsider the data from the previous study about the effect of specialized prenatal care for women with gestational diabetes. Do the data provide evidence of a relationship between the type of prenatal care a woman with gestational diabetes receives and whether or not she has an LGA baby?a.
Reconsider the data from the previous two exercises. Now investigate whether there is any association between coff ee drinking and the letter chosen to complete the four letter word.Data from previous exerciseCollege students were asked to indicate their sex, whether or not they drink coffee, and
Reconsider the data from the previous study about the effect of specialized prenatal care for women with gestational diabetes. Do the data provide evidence of a relationship between the type of prenatal care a woman with gestational diabetes receives and whether or not she has an LGA baby?a. Define
A baby weighing more than 4,000 g at birth is considered to be large for gestational age (LGA). Gestational diabetes in the mother is believed to be a common risk factor for LGA. In an article published in the New England Journal of Medicine (October 2009), researchers Landon et al. reported a
Reconsider the context of investigating whether giving chest-compression-only (CC) instructions rather than standard cardiopulmonary resuscitation (CPR) instructions to the witness of a heart attack will improve the victim’s chance of surviving. One of the randomized experiments that the
Reconsider the data from the previous exercise about investigating whether giving chest-compression-only (CC) instructions rather than standard cardiopulmonary resuscitation (CPR) instructions to the witness of a heart attack will improve the victim’s chance of surviving.a. Use an appropriate
Reconsider the data from the previous exercise about investigating whether giving chest-compression-only (CC) instructions rather than standard cardiopulmonary resuscitation (CPR) instructions to the witness of a heart attack will improve the victim’s chance of surviving.a. Which of the following
To investigate whether giving chest-compression-only (CC) instructions rather than standard cardiopulmonary resuscitation (CPR) instructions to the witness of a heart attack will improve the victim€™s chance of surviving, researchers Hupfl et al. (Th e Lancet, 2010) combined the results
Reconsider the data from the previous exercise about investigating whether there is a relationship between undergoing surgery and whether a man dies due to prostate cancer related reasons.a. Organize the counts in a well-labeled 2 × 2 table.b. Use an appropriate randomization-based applet to find
Reconsider the data from the previous exercise about investigating whether there is a relationship between undergoing surgery and whether a man dies due to prostate cancer related reasons.a. Which of the following is the appropriate null hypothesis? Choose one.A. Surgery recipients are equally
Researchers Wilt et al. (New England Journal of Medicine, 2012) investigated whether surgery, compared to just observation, was (more) effective in improving men’s survival chances aft er being diagnosed with prostate cancer. Th e researchers identified 731 men with localized prostate cancer who
Reconsider the exercise in Section 5.1 about school spirit (Exercise 5.1.3). Suppose that you find that 24% of a random sample of students at ESU wear clothing with the school name or logo, compared to 16% of a random sample of students at MSU. Our research question: Is the observed difference in
Reconsider the previous question about Medicare audits. A statistics student decides to use the Two Proportions applet to find a p-value to investigate whether there is an association between the size of a claim and whether it is judged to be an overpayment. Here is the output: a. The above
Reconsider the exercise in Section 5.1 about Medicare audits (5.1.6). Of the 30 small claims, 14 were judged to be over payments; of the 30 medium claims, 8 were judged to be overpayments. Our research question is this: “Does the chance that the claim is judged to be an overpayment tend to differ
Show that it is possible for Simpson’s paradox (see Exercise 5.1.23) to occur with two soft ball players. Produce a hypothetical example where one player (Amy) has a higher percentage of hits than another (Barb) in June, and Amy also has a higher percentage of hits than Barb in July. Yet when
In 1973 a lawsuit was filed against the University of California at Berkeley, alleging sex discrimination in its graduate admissions policies. The following table pertains to two of the graduate programs at the university. For each program, it lists the number of men accepted, the number of men
The following segmented bar graph was produced from data collected in the 2010 General Social Survey with regard to the question €œCan people be trusted?€a. About what proportion of the liberals responded that people can be trusted?b. About what proportion of the conservatives
The following two-way table classifies hypothetical hospital patients with a certain disease, according to the hospital that treated them and whether they survived or died:a. Calculate the proportion of Hospital A€™s patients who survived and the proportion of Hospital B€™s
Reconsider the data from the previous exercise. Now investigate whether there is any association between sex of respondent and the letter chosen to complete the four-letter word.Data from previous exerciseCollege students were asked to indicate their sex, whether or not they drink coffee, and what
College students were asked to indicate their sex, whether or not they drink coffee, and what letter they would use to complete the four-letter word beginning with F A I __ .Results are given in the following data table (* indicates a missing value):a. Produce a 2 × 2 table of counts
Many studies have shown that women who smoke while pregnant tend to have babies who weigh significantly less at birth, on average, than women who do not smoke while pregnant.a. Identify the population(s) of interest in these studies.b. Identify the explanatory variable in these studies. Also
Studies have shown that children in the U.S. who have been spanked have a significantly lower IQ score on average than children who have not been spanked.a. Identify the explanatory variable in these studies. Also classify this variable as categorical or quantitative.b. Identify the response
In July 2013, Gallup surveyed 2,027 randomly selected U.S. adults. They found that of the 921 people who described themselves as overweight, 424 reported having some or many friends/family members who were overweight (424/921 = 0.46). Also, of the 1,106 people who described their weight as being
Do men with children tend to live longer than men without children? To investigate, a group of students at Cal Poly randomly sampled men from the obituaries page on the San Luis Obispo Tribune’s webpage between June and November 2012. For each man selected, they noted the age at which the person
To investigate whether there is an association between happiness and income level, we will use data from the 2002 General Social Survey (GSS), cross classifying a person€™s perceived happiness with their family income level. The GSS is a survey of randomly selected U.S. adults who are not
A 2013 Gallup poll asked randomly selected U.S. adults whether they wanted to stay at their current body weight or change. One purpose was to investigate whether there was any difference between men and women with regard to this aspect.a. Identify the explanatory variable. Is it a categorical
Is there an association between political party affiliation and beliefs about human evolution? A survey of a random sample of U.S. adults by The Pew Research Center for the People and the Press conducted in March and April 2013 recorded each participant€™s political party affiliation and
A survey of a random sample of U.S. adults by The Pew Research Center for the People and the Press conducted in early January 2010 recorded each participant’s highest level of education completed and whether they knew that responding to the Census was required by law. Of the 973 participants who
In November 2010, an article titled “Frequency of Colds Dramatically Cut with Regular Exercise” appeared in Medical News Today. Th e article was based on the findings of a study by researchers Nieman et al. (British Journal of Sports Medicine, 2010) that followed 1,002 people aged 18–85 years
In February 2013, the Pew Research Center surveyed randomly selected U.S. adults about their opinions on gun ownership and related issues. One of the questions they asked was, “Should states be allowed to ignore federal gun laws?” Of the 366 Republicans, 57.9% (212/366) responded “yes,”
Researcher F.H. Messerli published an article titled “Chocolate Consumption, Cognitive Function, and Nobel Laureates” in the October 2012 issue of the New England Journal of Medicine. Th e article shows a positive association between a country’s chocolate consumption and the number of Nobel
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