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mathematics
introduction to business statistics

Questions and Answers of Introduction to business statistics

An eight-year cohort study of 3,454 initially disease-free men and women (ages around 60 years or more) recorded the extent of physical activity the participants engaged in and whether or not they
Refer to the previous exercise about the relationship between heart disease and baldness. The data are provided in the file HeartDiseaseAndBaldness.a. Compute the conditional proportions of heart
Recall Exercise 8.1.15 about the relationship between heart disease and baldness. The data are provided in the file HeartDiseaseAndBaldness.a. Identify the observational units.b. Describe the
Refer to the previous exercise about the study of the relationship between sleep apnea and hypertension. Suppose that the observed cell counts were actually three times as big as those reported in
Refer to the previous exercise about the study of the relationship between sleep apnea and hypertension. Show how to calculate the chi-square statistic by setting up the formula with appropriate
Refer to the previous exercise about the study of the relationship between sleep apnea and hypertension.a. State the appropriate null and alternative hypotheses in words.b. Explain why it would be
In a study of the relationship between sleep apnea and hypertension (New England Journal of Medicine, 2000), researchers Peppard et al. categorized the participants by the severity of sleep apnea at
Recall Exercise 8.1.12 about whether different generations view marriage differently. The corresponding data are available in the file MarriageViews.a. State the appropriate null and alternative
Refer to the previous exercise about the study of different HIV intervention programs. Suppose that the observed cell counts were actually twice as big as those reported in the original study. For
Refer to the previous exercise about the study of different HIV intervention programs. Show how to calculate the chi-square statistic by setting up the formula with appropriate numbers.Data from
Refer to the previous exercise about the study of different HIV intervention programs.a. State the appropriate null and alternative hypotheses in words.b. Explain why it would be okay to use the
Researchers Jemmott III et al. (Journal of American Medical Association, 1998) reported a study in which a group of inner-city African American adolescents from Philadelphia were randomly divided
Consider the chi-square statistic.a. Can the value of this statistic be negative? Why or why not?b. When will the chi-square statistic be 0?c. Which of (A)–(C) describes the shape of the
Suppose two surveys are done to see if Democrats, Independents, and Republicans differ on their agreement with a certain issue and the results are shown in the following two tables.a. Input the table
Read FAQ 8.1.1 and then reconsider Exercise 8.1.12 about whether different generations view marriage differently.a. If you were to compare two generations at a time, how many separate comparisons
Read FAQ 8.1.1 and then reconsider Exercise 8.1.29 based on Exploration 8.1, where you investigated whether there was evidence of an association between the type of default option and whether a
Reconsider Exercises 8.1.23 and 8.1.25 on cellphone and smartphone ownership. We considered our population to be that of all adults in the U.S. Now suppose we want the population to be all the
In a September 2013 poll conducted by the Pew Research Center, they asked a random sample of U.S. adults if they owned a smart phone. The results are shown in the following table by race.a. What
Reconsider the previous problem on cellphone use. Complete a test of significance to determine if there is an association between race and whether or not someone owns a cellphone using p̂max −
In a September 2013 poll conducted by the Pew Research Center, they asked a random sample of U.S. adults if they owned a cellphone. The results are shown in the following table by race.a. What
In a January 2014 Quinnipiac University poll the following question was asked to a random sample of U.S. voters: €œDo you support or oppose the health care law passed by Barack Obama and
Reconsider the previous problem on approval of stop and frisk. Complete a test of significance to determine if there is an association between age category and whether or not someone approves or
In a February 2013 Quinnipiac University poll the following question about a typical practice of the New York Police Department was asked to a random sample of New York City voters: €œAs
Reconsider the previous exercise about contagious yawning and time of day. Th e results of this test are not significant. If this study were redone, what suggestions do you have that would help make
Student researchers wanted to see if it there was an association between the time of day and whether or not someone would yawn right aft er seeing another person yawn. To gather their data, they
Researchers at the University of Pennsylvania studied the humor of late-night comedians Jon Stewart, Jay Leno, and David Letterman. Between July 15 and September 16, 2004, they performed a content
In Exploration 8.2B, we will look at a study that was done to determine if there is an association between the amount of light in infants€™ bedrooms at night (darkness, night light, room
Many studies have been done to look at the relationship between heart disease and baldness. In one study, researchers selected a sample of 663 heart disease male patients and a control group of 772
Reconsider the previous exercises. If the different generations did not view marriage differently what would you expect the cell counts in the 8.1.14 table to be? (That is, there is no association
Reconsider the previous question on how different generations view marriage. The results are shown in thetable in the previous exercise and can also be found in the file MarriageViews.a. Identify the
Do different generations view marriage differently? A 2010 survey of a random sample of adult Americans conducted by the Pew Research Center asked the following question of each participant:
Suppose 100 students are asked if the cellphone they use is a smartphone or a basic phone and the 8.1.11 two-way table summarizes the results.a. Find the proportion of males that own smartphones and
Suppose you want to compare proportions of adults who have donated blood within the past year among California, Iowa, Massachusetts, and Michigan residents. You take a random sample of 200 adults
Suppose that you want to compare proportions of registered Democrats, Independents, and Republicans who have donated blood within the past year.a. Which would be appropriate for this study: random
Suppose a poll is done to see if voters agree with a new law passed in Congress. The results are summarized in the 8.1.8 table along with the voters€™ party affiliation. You plan to test to
Consider the MAD statistic. What would happen if you did not take absolute values before calculating the sum of differences between group proportions? Why would this not be a useful calculation
Given the four sample proportions 0.66, 0.45, 0.73, and 0.44, determine the MAD statistic.
Given the three sample proportions 0.25, 0.30, and 0.35, determine the MAD statistic.
What has to be true about the observed proportions if the MAD statistic is zero?
Null distributions using the MAD statistic will be:A. Symmetric and centered at zero.B. Symmetric and centered at the MAD statistic.C. Skewed right.D. Skewed left
Is the sample large enough to use a theory-based test?As mentioned earlier, sand is used in the filter. Different filters had different amounts of sand.The students split the filters into two groups:
Identify the explanatory and response variables in this study. Classify the variables in this study as categorical or quantitative.As mentioned earlier, sand is used in the filter. Different filters
The “Reading the Mind in the Eyes Test” (RMET) measures the ability of a person to infer the mental state of another from looking at facial expressions. Researchers Domes et al. (Biological
The Cholesterol Level data sets give cholesterol levels of heart attack patients. Cholesterol measures are taken 2, 4, and 14 days aft er a patient has suffered a heart attack. Is there a significant
The Cholesterol Level data sets give cholesterol levels of heart attack patients. Cholesterol measures are taken 2, 4, and 14 days aft er a patient has suffered a heart attack. Is there a significant
In June 2012, Time magazine ran an article titled “Do Family Dinners Really Reduce Teen Drug Use?” Answer the following questions in this context.a. Identify the observational units.b. Identify
Based on a survey of almost 3,000 adults, researchers Wyatt et al. (Obesity Research, 2002) reported that those who ate breakfast regularly tended to be more successful at maintaining their weight
In a study published in Preventive Medicine (1991), researchers Stampfer and Colditz observed that women who underwent hormone replacement therapy (HRT) showed a lower risk of coronary heart disease
A Gallup poll conducted in December 2013 found that 74% of respondents who were 65 years or older owned a VCR compared to 41% of 18- to 29-year olds.a. Identify the explanatory variable.A.
Based on a four-year (2003–2007) study of over 30,000 people who were 45+ years, where all individuals were followed up regularly for diet and health changes, researchers Tsivgoulis et al.
Regarding the previous question about number of TVs and life expectancy:a. Identify the observational units.A. PeopleB. Number of TVs per 1,000 peopleC. CountriesD. Life expectancyb. Identify the
Based on this study, is it reasonable to conclude that by sending TVs to countries with lower life expectancies, we can increase their inhabitants’ lifetimes? If yes, explain how. If no, give an
Studies conducted in New York City and Boston have noticed that more heart attacks occur in December and January than in all other months. Some people have tried to conclude that holiday stress and
Do different generations view marriage differently? A 2010 survey conducted by the Pew Research Center asked the following question of each participant: €œIs marriage becoming
In a study published in a 2007 issue of the journal Preventive Medicine, researchers found that smokers were more likely to have used candy cigarettes as children than nonsmokers were. When hearing
Reconsider the previous exercise about the potential confounding variable that provides an alternative explanation for why the all-nighter group would have a significantly lower average GPA. Sketch a
Reconsider the previous study about GPAs and pulling all-nighters. Suppose that the difference between these two averages (3.1 vs. 2.9) is shown to be statistically significant. Which of the
Researchers found that students who claimed to have never pulled an all-nighter had an average GPA of 3.1, compared to 2.9 for those students who do claim to have pulled all-nighters.a. In this
Summarize your findings. If you were to repeat this study, are there any changes or improvements you would make? What additional questions might you be interested in asking?Let’s use our 3S
Now, let’s step back a bit and think about the scope of our inference. What are the wider implications? Do you think that your conclusion holds true for people in general?
If you were to construct a 99% confidence interval like the 95% confidence interval you constructed in #18 by testing different values for π and seeing whether or not they are plausible, how would
What would happen to your 95% confidence intervals if the sample size had been 1,000 instead of 242 but still 52% of your sample stated they had talked on a cell phone while driving? Use the applet
Finally, use the Th eory-Based Inference applet to find a 95% confidence interval for the population proportion of drivers 16 to 17 who have ever talked on a cell phone while driving.a. What is the
Now use the One Proportion applet to create an interval of plausible values with 95% confidence for the population proportion of drivers 16 to 17 who have ever talked on a cell phone while driving
Use the One Proportion applet to create an interval of plausible values with 95% confidence for the population proportion of drivers 16 to 17 who have ever talked on a cell phone while driving. Do
You should have seen that 0.50 is a plausible value for the true proportion of all 16- to 17-year-olds who have used their cell phones while driving. Does this prove that 0.50 is the true
Summarize the conclusion that you draw from this study and your simulation analysis. Also explain the reasoning process behind your conclusion.Let’s use our 3S strategy to help us investigate how
Determine the approximate p-value from your simulation analysis. Also interpret what this p-value represents (i.e., the probability of what, assuming what?).Let’s use our 3S strategy to help us
How do the actual study results compare to the null distribution obtained when simulating the chance model? Do you believe the study results provide convincing evidence against the “equally likely
Based on the dotplot generated using the 1,000 possible values of the statistic, what values would you consider typical values and what would you consider atypical values of the statistic when the
What is the center of your simulated null distribution? Does it make sense that this is the center? Explain.Let’s use our 3S strategy to help us investigate how much evidence the sample data
Use the One Proportion applet to simulate 1,000 repetitions of this study, assuming that every driver is just as likely to talk on the cell phone as not while driving. Report what values you input
How many of the 16- to 17-year-olds in the sample have ever talked on their cell phone while driving?The survey found that 52% of the 242 16- to 17-year-olds had talked on the phone while driving.
State the appropriate null and alternative hypotheses to be tested.Th e survey found that 52% of the 242 16- to 17-year-olds had talked on the phone while driving.To help answer this question Pew
Is it possible that we could observe the statistic from this sample of 242 drivers even if all of the drivers were just as likely as not to have talked on the cell phone while driving? Why?Let’s
If we assume that each driver is equally as likely to have talked on the cell phone while driving as not, what is the chance that a randomly selected individual will have talked on the cell phone
Is the sample proportion who have talked on their cell phone while driving greater than 0.50? (If not, there’s no need to conduct a simulation analysis. You will not have convincing evidence that a
What is the statistic that you can use to summarize the data collected in the study?Let’s use our 3S strategy to help us investigate how much evidence the sample data provide to support our
Describe the parameter of interest in words. (You can use the symbol π to represent this parameter.)To help answer this question Pew Research(2009) conducted a survey of nationally representative
What is the variable that is measured/recorded on each observational unit?To help answer this question Pew Research(2009) conducted a survey of nationally representative 242 cell phone users ages 16
What are the observational units?To help answer this question Pew Research(2009) conducted a survey of nationally representative 242 cell phone users ages 16 to 17 years and asked whether they had
Identify the research question and state it as a conjecture.Drivers today have many more distractions to deal with than drivers of a century ago. Let’s focus on new drivers aged 16 to 17. Do you
In the mid-1980s, sociologist Shere Hite undertook a study of American women’s attitudes toward relationships, love, and sex by distributing 100,000 questionnaires in women’s groups. One of the
Suppose that you look up the diameters of the planets in our solar system and use the data to determine a 95% confidence interval. Would the resulting interval make any sense? Explain why or why not.
Reconsider the previous two exercises. A 95% confidence interval for the population mean difference in ages (husband–wife, in years) turns out to be (0.92, 2.92). For each of the following,
Reconsider the previous exercise.a. Based on the dotplot, determine the sample proportion of married couples for whom the wife is older than the husband.b. Is it valid to use a theory-based procedure
Reconsider the previous exercise. Answer parts (a) to (e) with regard to margin of victory rather than total number of goals. Data can be found in the file called Hockey2 on the textbook website.Data
A student went to the local county courthouse (in Cumberland County, Pennsylvania, in June and July of 1993) to gather data on ages of soon-to-be husbands and wives who had recently applied for
Suppose you have very little knowledge about professional ice hockey, but you want to get a sense of how many goals are scored per game on average and what a typical margin of victory is. You decide
Reconsider the previous exercise.a. Suppose the sample standard deviation of the expected spending amounts was $30. Determine and interpret a 95% confidence interval for the population mean.b. Now
The National Retail Federation conducted a national survey of 8,526 consumers on September 1–9, 2009. Among the findings reported were that:• 29.6% of those surveyed said that the state of the
Refer to the previous exercise. The report from the Pew Research Center also provided survey results for different age groups:• Among those aged 18 to 29, 89% of 395 used social networking
In May of 2013, the Pew Research Center’s Internet and American Life Project conducted a survey with a random sample of American adults. Of the 1,895 Internet users in the sample, 72% reported that
An instructor wants to find the proportion of international students at his school. He contacts the registrar’s office and obtains enrollment data for the year 2011. Using these data, he reports
Suppose that Elsa and Frank determine confidence intervals based on the same sample proportion and sample size. This time, Elsa uses a larger confidence level than Frank. How will midpoint and width
Suppose that Elsa and Frank determine confidence intervals using the same confidence level, based on the same sample proportion. Elsa uses a larger sample size than Frank. How will midpoint and width
A Pew Research (2009) survey of nationally representative 242 cell phone users, ages 16 to 17 years, found that 52% had talked on the phone while driving.a. Use these data to estimate, with 95%
An article, “Foul drinking water aboard airlines worsens,” in The Seattle Times (January 2005) reported that 29 out of 169 water specimens from randomly selected passenger aircraft carrying
Reconsider the previous three exercises. Now suppose that the player has actually become a .400 hitter. Make this change to the alternative value (with a significance level of 0.10 and a sample size
Reconsider the previous two exercises. Change the significance level to 0.10 (with a sample size of 100 at-bats), and answer Questions (a) to (d). Then describe the effect of decreasing the

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