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mathematics
introduction to business statistics

Questions and Answers of Introduction to business statistics

From Exercise 5.2.19, recall the results from a 2013 Gallup poll that asked randomly selected U.S. adults whether they wanted to stay at their current body weight or change. Of the 562 men surveyed,
From Exercise 5.2.22, recall the survey of a random sample of U.S. adults by Th e Pew Research Center for the People and the Press conducted in early January 2010 that recorded each participant’s
Recall Exercise 5.2.27 about an Italian firm Ma-Vib that was in the news for “sexual discrimination” for having chosen only its female employees to be dismissed. Before the layoffs, Ma-Vib
Researchers Penninx et al. (Archives of General Psychiatry, 2001) looked at the relationship between depression and a person’s ability to survive cardiac disease. The researchers identified 450 men
In a randomized, double-blind study reported in the Journal of American Medical Association, researchers Waber et al. (2008) administered a pill to each of 82 healthy paid volunteers from Boston,
The Physicians’ Health Study is a very large, randomized study designed to “test the effects of low-dose aspirin… in the prevention of cardiovascular disease (CVD).” The subjects were 22,071
Recall the data from the Physicians’ Health Study: Of the 11,034 physicians who took the placebo, 189 suffered heart attacks during the study. Of the 11,037 physicians who took aspirin, 104 had
Recall the data from the Physicians€™ Health Study: Of the 11,034 physicians who took the placebo, 189 suffered heart attacks during the study. Of the 11,037 physicians who took aspirin,
Recall the data from the Physicians’ Health Study: Of the 11,034 physicians who took the placebo, 189 suffered heart attacks during the study. Of the 11,037 physicians who took aspirin, 104 had
Another outcome of interest in the Physicians’ Health Study was whether the subjects developed ulcers or not. Of the 11,034 physicians who took the placebo, 138 developed ulcers during the study.
Recall the data from the Physicians’ Health Study: Of the 11,034 physicians who took the placebo, 138 developed ulcers during the study. Of the 11,037 physicians who took aspirin, 169 developed
Recall the data from the Physicians€™ Health Study: Of the 11,034 physicians who took the placebo, 138 developed ulcers during the study. Of the 11,037 physicians who took aspirin, 169
Recall the data from the Physicians’ Health Study: Of the 11,034 physicians who took the placebo, 138 developed ulcers during the study. Of the 11,037 physicians who took aspirin, 169 developed
Suppose that you collect data on two categorical variables and summarize the results in a 2 Ã— 2 table of counts such as the following:Your goal is to decide if the data provide strong
Reconsider the previous exercise.a. If the observed proportion of successes turns out to be the same for both groups, would you expect the p-value to be very small, somewhat small, or not small at
Explain why the methods of this chapter are not appropriate for investigating the following research questions:• Have teenagers in the United Kingdom read more Harry Potter books, on average, than
Psychologists investigated whether praising a child€™s intelligence, rather than praising his/her effort, tends to have negative consequences such as undermining their motivation (Mueller
Professional baseball teams have one coach at first base and one coach at third base, with third base regarded as the more important and prestigious position. An article in the August 11, 2010, New
A study conducted in 2002 by Shiff man, Dressler, Hajeh, and Gilburt investigated whether a nicotine lozenge is helpful for smokers trying to quit smoking. The researchers recruited smokers who were
Reconsider the previous exercise. At the end of the 52-week study, 17.9% of those in the nicotine group had successfully abstained from smoking, compared to 9.6% of those in the placebo group.a.
Reconsider the previous two exercises.a. Determine a 95% confidence interval for the difference in long-run probabilities of successfully abstaining from smoking between the two groups.b. Interpret
Reconsider the previous three exercises. Now consider only the results for the nicotine lozenge, not for the placebo.a. Determine a 95% confidence interval for the probability that a smoker who uses
A survey conducted by the Gallup organization in 1999 asked American adults whether they are satisfied with their physical attractiveness or wish they could be more attractive. The survey found that
Reconsider the previous exercise.a. Suppose that the study had included 100 people of each sex. Determine the test statistic and p-value for testing whether the proportions who are satisfied with
The Nellie Mae organization conducts an extensive annual study of credit card usage by college students. For their 2004 study, they analyzed credit bureau data for a random sample of 1,413
Reconsider the previous exercise.a. Determine a 90% confidence interval for the difference in proportions of undergraduates who held a credit card between the years 2001 and 2004.b. Repeat (a) with a
Reconsider the previous two exercises.a. Describe what a Type I error would mean in this context.b. Describe what a Type II error would mean in this context.Data from previous exercisesThe Nellie Mae
Reconsider the previous three exercises.a. Describe what power means in this study.b. Would you expect that you could increase the power of a test by using a larger sample size or a smaller sample
The General Social Survey (GSS) is a large-scale national survey conducted every two years with a representative group of American adults. The 2 Ã— 2 table below shows results from the
Reconsider the previous exercise. Using the same data but grouping €œroutine€ with €œexciting€ rather than with €œdull€ produces the
Is this study an experiment or an observational study? How are you deciding?
What are the variables that are measured/recorded on each unit?
Describe the parameters of interest in words. (You can use the symbol π to represent these parameters.)
State the null and alternative hypotheses for a test of significance to see whether this experiment provides statistically significant evidence that Vitamin C prevented colds in the skiers. Use a
Of the 139 skiers assigned to take Vitamin C, 17 developed a cold. Of the 140 skiers assigned to take a placebo, 31 developed a cold. Fill in the 2 Ã— 2 table provided. Placebo Total
Incidence is the term used to describe the percent of the sample who onset with an illness over a certain time period. In this case, the incidence rates are the same as the conditional proportions.
What is the difference in incidence rates in the two groups? Before doing a test of significance, comment on whether you think this is evidence that Vitamin C prevents colds.
As observed proportions move farther apart:A. Both the MAD statistic and the p-value will decrease.B. Both the MAD statistic and the p-value will increase.C. The MAD statistic will increase and the
Which of the following are true about the MAD statistic? There may be more than one statement that is true.a. The MAD statistic can never be negative.b. The MAD statistic is the average distance
You should have found that 1,000 mL/min is a plausible value for average flow rate for the population of all similar water filters. Does this mean that all the filters have flow rates of about 1,000
Carry out an appropriate test of significance to see whether the Cameroon water filters (population) tend to fl ow at a rate different than 1,000 mL/min, or is an average of 1,000 mL/min plausible?
Use the Descriptive Statistics applet to create a dotplot of the flow rates. Include average and standard deviation for the fl ow rate. What do you observe?
List some similarities and differences between this research question and our first research question looking at the average difference in first and second E. coli counts.Let’s look at one last
Are the samples of the first E. coli count independent or dependent of the samples of the second E. coli count? Explain.As mentioned earlier, sand is used in the filter. Different filters had
What are the average E. coli counts for each sand level? Are the counts higher or lower with the higher level of sand in the filter? Also give the standard deviations for the E. coli counts for each
Discuss the study design. Why does pairing make sense here? What would you do differently to improve upon this study? What further research would you propose based on your findings from this
Can generalizations be made to a larger population? Is there a cause-effect relationship between the variables?There are several research questions we will ask in this investigation. The first one
Based on your p-value and confidence interval, what conclusions can you draw from this test?There are several research questions we will ask in this investigation. The first one is: On average, is
Carry out an appropriate test of significance to see whether, on average, there is a genuine diff erence between the fi rst E. coli count and the second E. coli count. Report your -value and a
What is the average of the diff erence (Day 1 – Day 2) in E. coli counts? Does the sign of this average correspond to your answer of increasing or decreasing between Day 1 and Day 2 in the previous
What are the average E. coli counts for each day? Did the E. coli in the sample increase or decrease on average from Day 1 to Day 2? Explain. Also give the standard deviations for the E. coli counts
State the null and alternative hypotheses to be investigated with this study in symbols or in words.
Could the sample size of 14 be large enough to give a valid p-value from a theory-based test of significance?There are several research questions we will ask in this investigation. The first one is:
Are the samples of the first E. coli count independent or dependent of the samples of the second E. coli count? Explain. Based on your answer, is this an independent samples or paired design?There
Identify the role of these variables (explanatory, response). Classify the variables in this study as categorical or quantitative.There are several research questions we will ask in this
What variables are measured/recorded on each observational unit?There are several research questions we will ask in this investigation. The first one is: On average, is there a significant difference
What are the observational units?There are several research questions we will ask in this investigation. The first one is: On average, is there a significant difference in the E. coli counts between
Reconsider the previous three exercises.a. Even though it€™s not an appropriate analysis, perform a two-sample t-test (rather than the appropriate paired t-test) on the data. Report the
Reconsider the previous two exercises.a. Use the simulation analysis to produce a 95% confidence interval for the relevant parameter. Interpret what the interval reveals.b. Determine a 95%
Reconsider the previous exercise.a. Comment on whether the conditions for applying a theory-based paired t-test are satisfied.b. Regardless of your answer to part (a), conduct a theory-based paired
A student who did volunteer work at an animal shelter wanted to see if cats really respond aggressively to catnip (Jovan, Stats magazine, 1999). Using a sample of 15 cats, she recorded how many
Reconsider again the baseball data from Example 7.2.a. Repeat the previous exercise, this time producing a 95% confidence interval first based on the actual matched pairs data and then based on
Reconsider again the baseball data from Example 7.2.a. Perform the appropriate (theory-based) matched pairs t-test. Report the hypotheses, test statistic, and p-value. Summarize your conclusion.b.
Reconsider the baseball data from Example 7.2 (FirstBase). Suppose for now that the data had been from 44 different players rather than paired data on the same 22 players. Test whether one of the
Humans are able to collaborate on projects to accomplish their goals. What about chimpanzees? Do chimpanzees know when they need to recruit help in order to solve a problem and when they are able to
During one semester of a healthy living class taught at Hope College, students were weighed (in kilograms), were weighed under water (in kilograms), and had their body fat percentage calculated.
During one semester of a healthy living class taught at Hope College, students measured how flexible they were in terms of inches reached while sitting. Flexibility was measured at the beginning of
Suppose that a company has developed a new method of water proofing boots that it wants to compare in an experiment against a standard method.a. Describe how to conduct a randomized experiment
Suppose that a student wants to gather data to investigate whether husbands tend to be older, on average, than their wives. Th e student obtains a sample of 200 marriage licenses that report the ages
Suppose that a restaurant owner wants to investigate whether the type of music played in the background affects how much customers spend on their meals. The owner plans to play classical music on
Some smoke alarms for homes with children now use a recording of the mother’s voice calling the child by name, as opposed to the beeping sound of conventional smoke alarms.a. Describe how you could
For each of the following studies, indicate whether the data were collected in a paired manner and therefore require a paired analysis.a. A farmer wants to know whether hand-milking or
Clearly describe what, if anything, is incorrect about each of the following hypotheses.a. H0: p̂1 – p̂2 = 0 versus Ha: p̂1 – p̂2 ≠ 0b. H0: μ = 40 versus Ha: μ < 30c. H0: π1 − π2 =
Does your bowl size influence how much you eat? To investigate, researchers recruited undergraduates from a large university to participate in a study that was conducted over several days. Th e
Match each question with the proper significance test (from (A) − (D)) needed to answer the question.a. _____ Do a majority of students at your college prefer chocolate soft serve ice cream to
Refer to the previous exercise about the effect of oxytocin on the ability to infer the mental state of others, as measured by the RMET score. Recall that for the sample of 30 participants, the
In a study of the effect of tomoxetine as an alternative treatment for attention deficit hyperactivity disorder (ADHD), researchers Spencer et al. (The American Journal of Psychiatry, 1998) recruited
Recall Example 7.3 about the number of M&Ms taken with small versus large bowls. The example uses the following parameter of interest:μd = Long-run mean difference for the number of M&Ms
Recall Exploration 7.1 and Example 7.2 about the time needed to round first base using the narrow angle versus the wide angle. Th e previous exercise reports the summary statistics for the difference
Recall Exploration 7.1 and Example 7.2 about the time needed to round first base, using the narrow angle versus the wide angle. Here are the summary statistics on the difference in times (narrow
Recall the previous exercises about estimating energy expenditure. The summary statistics on the difference between estimated EE and actual EE were as follows:Suppose the summary statistics had
Recall the previous exercises about estimating energy expenditure. The summary statistics on the difference between estimated EE and actual EE were as follows:Suppose the summary statistics had
Recall the previous exercises about estimating energy expenditure. The summary statistics on the difference between estimated EE and actual EE were as follows:Suppose the summary statistics had
Recall the previous exercises about estimating energy expenditure. Previously you carried out a theory-based matched pairs test to investigate whether, on average, men in the study significantly
Recall the previous exercise about estimating energy expenditure (EE). The previous exercise also reports the summary statistics for the difference in EE (estimate ˆ’ actual).a. Use the
How many calories do you think you burn or expend with 60 minutes of walking on the treadmill? An article that appeared in the American Journal of Men€™s Health (2010) presented the results
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
Refer to the previous exercises about investigating whether infants tend to look at surprising events or behavior for longer times, on average, compared to uninteresting ones? Given below are the
Refer to the previous exercises about investigating whether infants tend to look at surprising events or behavior for longer times, on average, compared to uninteresting ones? Given below are the
Refer to the previous exercises about investigating whether infants tend to look at surprising events or behavior for longer times, on average, compared to uninteresting ones? Given below are the
Refer to the previous exercise about investigating whether infants tend to look at surprising events or behavior for longer times, on average, compared to uninteresting ones?a. Define, in words, the
Researchers Hamlin et al. (Nature, 2007) conducted a study with 16 infants that involved an assessment of infants€™ expectations of a climber toy€™s attitude towards a
Refer to the previous exercises about the study of parents’ perceptions of their children’s size. The researchers Kaufman et al. (Current Biology, 2013) also surveyed a sample of 38 parents about
Refer to the previous exercise about the study of parents’ perceptions of their children’s size by researchers Kaufman et al. (Current Biology, 2013). Recall that the sample of 39 parents
In a study of parents’ perceptions of their children’s size, researchers Kaufman et al. (Current Biology, 2013) asked parents to estimate their youngest child’s height. The researchers
Refer to Exercise 7.2.12 where a student wanted to investigate whether or not people tend to marry spouses of similar ages and so gathered age data from a sample of 24 couples taken from marriage
Design your own experiment: Develop the plan for the investigation of a research question that would be best answered using paired data.a. State the research question.b. Explain how pairing will be
Reconsider the previous exercises on handedness and reaction time. If you haven’t already done so, put the data file Reaction Times into the Matched Pairs applet and do at least 1,000
Reconsider the previous exercise on handedness and reaction time. If you haven’t already done so, put the data file Reaction Times into the Matched Pairs applet and do at least 1,000
Student researchers wanted to see if a person’s reaction time is slower if they use their nondominant hand to click a computer mouse compared to using their dominant hand. The researchers had a

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