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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
Is random sampling or random assignment the more important consideration if the research question is whether students tend to receive higher scores on essays if they are encouraged to submit a draft than if they are not so encouraged?
How would the p-value have changed if the alternative hypothesis was stated as: Alt: The long-run proportion of men who will call the researcher among those who cross the suspension bridge is different from that among those who cross the solid wood bridge.
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. Use an
Recall Exercise 5.2.32 about the study conducted to investigate the effects of €œromantic lyrics on compliance with a courtship request.€ 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
Recall Exercise 5.2.4 where 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 after being diagnosed with prostate cancer. The researchers identified 731 men with
Recall Exercise 5.2.7 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. Researchers Hupfl et al. (The Lancet, 2010)
Recall Exercise 5.2.11 about the link between babies being large for gestational age (LGA) and gestational diabetes in the mother. In an article published in the New England Journal of Medicine (October 2009), researchers Landon et al. reported on a study of 958 women diagnosed with mild
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.
Recall a study from Exercise 5.2.15 , called €œPower Posing: Brief Nonverbal Displays Aff ect Neuroendocrine Levels and Risk Tolerance,€ that was published in Psychological Science, September 2010, and describes an experiment involving 42 participants (male and female), where
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, 242 wanted to stay at their current weight, whereas of the 477 women surveyed, 172 wanted to stay at
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 highest level of education completed and whether they knew that responding to the Census was required
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 employed 18 women and 12 men; it then fired 15 of the women and none of the men. Is it valid to use the
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 and women with cardiac disease, evaluated them for depression, and followed them for four years. In
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, Massachusetts, but told half of them that the drug had a regular price of $2.50 per pill, whereas the
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 U.S. male physicians (aged 40–84 years, in the year 1982), who were randomly assigned to be in
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 heart attacks.a. Define the parameters of interest. Assign symbols to these parameters.b. State the
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 heart attacks.a. Recall that the formula for the standardized statistic in this scenario
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 heart attacks.a. Calculate the observed value of the relative risk of heart attacks comparing
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. Of the 11,037 physicians who took aspirin, 169 developed ulcers.a. Identify the explanatory and
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 ulcers.a. Define the parameters of interest. Assign symbols to these parameters.b. State the
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 ulcers.a. Recall that the formula for the standardized statistic in this scenario isPlug in
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 ulcers.a. Calculate the observed value of the relative risk of ulcers comparing physicians who took
Suppose that you collect data on two categorical variables and summarize the results in a 2 × 2 table of counts such as the following:Your goal is to decide if the data provide strong evidence that Group A and Group B diff er with regard to the long-run proportion of success.a. Is it
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 all? Explain.b. If Group A results in only successes and Group B results in only failures, would you
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 teenagers in the United States?• Do cows tend to produce more milk, on average, when they are
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 and Dweck, 1998). Children participating in the study were given a set of problems to solve. After
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 York Times raised a concern that minority coaches are underrepresented at third base compared to
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 interested in quitting through advertisements near four sites in the United Kingdom and 11 sites in
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. Produce a 2 × 2 table of counts to represent these data.b. Create a relevant graph to display the
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 what this interval reveals. Be sure to address the question of whether the data provide strong
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 nicotine lozenge will successfully abstain from smoking for 52 weeks.b. Based on this confidence
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 71% of women and 81% of men responded that they were satisfied with their attractiveness.a. Could
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 their attractiveness diff er significantly between the two sexes using a theory-based test.b. Now
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 undergraduate students between the ages of 18 and 24. They found that 76% of the students sampled held a
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 95% confidence interval.c. Repeat (a) with a 99% confidence interval.d. Which (if any) of these
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 organization conducts an extensive annual study of credit card usage by college students. For their
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 size? Explain.c. Would you expect that using a smaller (more strict) significance level would increase
The General Social Survey (GSS) is a large-scale national survey conducted every two years with a representative group of American adults. The 2 × 2 table below shows results from the 2010 survey regarding sex and whether the respondent considers life to be exciting:Analyze these data
Reconsider the previous exercise. Using the same data but grouping €œroutine€ with €œexciting€ rather than with €œdull€ produces the following 2 × 2 table:Analyze these data to investigate the question of whether men and
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 one-sided test.
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 × 2 table provided. Placebo Total Vitamin C No cold Cold 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. Find the incidence rates for individuals who received Vitamin C and those who received the placebo.
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 p-value will decrease.D. The MAD statistic will decrease and the p-value will increase.
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 sample proportions are from each other.c. The MAD statistic is the average of a group of sample
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 mL/min? Is testing a single mean here really telling us what we need to know about these filters?
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? State your hypotheses, 95% confidence interval, p-value, and conclusions.Let’s look at one last
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 research question. As a general rule, the flow rate of a water filter in good working condition should
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 different amounts of sand.The students split the filters into two groups: those that had more than 2 inches
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 sand level.As mentioned earlier, sand is used in the filter. Different filters had different amounts
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 study?There are several research questions we will ask in this investigation. The first one is: On average,
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 is: On average, is there a significant difference in the E. coli counts between the water that has
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 there a significant difference in the E. coli counts between the water that has just been filtered and
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 95% confidence interval.There are several research questions we will ask in this investigation. The
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 question? Explain. Also give the standard deviation for the differences in E. coli counts.There are
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 for each day.There are several research questions we will ask in this investigation. The first one
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: On average, is there a significant difference in the E. coli counts between the water that has just
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 are several research questions we will ask in this investigation. The first one is: On average, is
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 investigation. The first one is: On average, is there a significant difference in the E. coli counts between the
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 in the E. coli counts between the water that has just been filtered and water that is sitting in
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 the water that has just been filtered and water that is sitting in the bottom of a filter after it
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 hypotheses, test statistic, and p value. Summarize the conclusion that you would draw if this were 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% theory-based paired t-interval for the relevant parameter. Interpret what the interval reveals.Data from
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 t-test. Report the test statistic and p-value.c. Summarize your conclusion about strength of evidence
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 €œnegative interactions€ (such as hissing or clawing) each cat engaged in during a
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 assuming that the data were from 44 different players rather than the same 22 players.b. Comment on how
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. Now suppose that the data had been from 44 different players rather than the same 22 players. Perform
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 methods is significantly different than the other.a. Perform a simulation of a randomization test to
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 solve it on their own? Researchers placed a food platform outside of the chimpanzee’s cage. They
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. These were all done at the beginning of the semester and again at the end of the semester. We will
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 the semester and again at the end of the semester. We will consider this a representative sample 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 without pairing to compare the two methods of water proofing boots.b. Describe how to conduct a matched
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 of both the husband and wife. The student randomly selected 100 of the marriage licenses and
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 evenings and contemporary music on other evenings for a total of two weeks, comparing the amounts
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 design a matched pairs study to investigate whether the new smoke alarms reduce the time needed for
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 machine-milking tends to produce more milk from cows. He examines records of how much milk the cows have produced
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 = 0 versus Ha: π1 − π2 < 0
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 participants were not told about the goal of the study until the very end of the data collection process.
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 vanilla?b. _____ Is the proportion of females at your college who participate in varsity athletics
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 researchers noted that the average increase in RMET score when on oxytocin compared to when on 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 men and women diagnosed with ADHD. All participants were administered tomoxetine and a
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 that will be taken when using a small bowl minus a large bowl.The hypotheses are H0: μd = 0 versus Ha:
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 in times (narrow ˆ’ wide).a. Use the formula of the standardized statisticcalculate its
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 ˆ’ wide) for the 22 players:a. Use an appropriate theory-based method to investigate whether
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 been:How, if at all, would the values of the following (using the theory-based method) be different?a.
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 been:How, if at all, would the values of the following (using the theory-based method) be different?a.
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 been:How, if at all, would the values of the following (using the theory-based method) be different?a.
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 overestimated or underestimated their EE. Here are a few more summary statistics.a. Use the Theory-Based
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 formula of the standardized statisticto calculate its value. Interpret the value of the standardized
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 of a study conducted by researchers Harris and George, whose objective was to evaluate how
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 difference between day 2 cholesterol measures and day 4 cholesterol measures? Carry out a
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 summary statistics for the difference (hinderer ˆ’ helper) in looking times (seconds).Suppose
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 summary statistics for the difference (hinderer ˆ’ helper) in looking times (seconds).Suppose
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 summary statistics for the difference (hinderer ˆ’ helper) in looking times (seconds).
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 appropriate parameter(s) of interest in the context of the study. Also, state the appropriate
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