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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
Reconsider the study mentioned in the previous exercise about guessing the size of Milwaukee’s population. Our research question: On average, will students like the ones in the study tend to guess a higher population size for Milwaukee if they are told about Chicago’s population size rather
In a survey of introductory statistics students, an instructor asked her students how many flip-flops they have. Suppose that the intent is to study whether there is an association between number of flip-flops and a persons sex. a. Identify whether the study is an experiment or an
Reconsider the previous exercise about the study of whether there is an association between number of flip-flops and a person’s sex.a. Use the information available in the previous exercise to find a standardized statistic to test whether the average number of flip-flops men have is different
Reconsider the previous exercises about the study of whether there is an association between number of Facebook friends and a person’s sex. The p-value for the randomization-based test of whether the average number of Facebook friends men have is different from that of women turns out to be
Reconsider the previous exercises about the study of whether there is an association between number of Facebook friends and a person’s sex.a. Use the 2SD method and the information available in the previous exercises to find a 95% confidence interval for the difference in average number of
Reconsider the previous exercises about the study of whether there is an association between number of Facebook friends and a persons sex. The following is output from carrying out the randomization test using the Multiple Means applet.Recall that the summary statistics about the data
In a survey of introductory statistics students, an instructor asked her students how many flip-flops they have. Suppose that the intent is to study whether there is an association between number of fl ip-fl ops and a persons sex.a. Identify whether the study is an experiment or an
Reconsider the previous exercise about the study of whether there is an association between number of flip-flops and a person’s sex.a. Use the information available in the previous exercise to find a standardized statistic to test whether the average number of flip-flops men have is different
Reconsider the previous exercises about the study of whether there is an association between number of flip-flops and a person’s sex. The p-value for the randomization-based test of whether the average number of flip-flops men have is different from that of women turns out to be 0.001.a.
Reconsider the previous exercises about the study of whether there is an association between number of flip flops and a person’s sex.a. Use the 2SD method and the information available in the previous exercises to find a 95% confidence interval for the difference in average number of flip-flops
Reconsider the previous exercise about the study of whether there is an association between number of flip-flops and a persons sex. The following is output from carrying out the randomization test using the Multiple Means applet. Recall that the summary statistics about the data
Anchoring is the common human tendency to rely too heavily, or anchor, on one trait or piece of information when making decisions. (Source: Wikipedia.) A group of students taking an introductory statistics course at a four-year university in
Reconsider the study mentioned in the previous exercise about guessing the size of Milwaukee’s population. Do the data provide evidence of the anchoring phenomenon among students like the ones in this study? That is, our research question is: On average, will students like the ones in the study
Reconsider the study mentioned in the previous exercise about guessing the size of Milwaukee’s population. Do the data provide evidence of the anchoring phenomenon among students like the ones in this study? Suppose that instead of comparing the average guess for Milwaukee’s population (Chicago
Do men with children tend to live longer, on average,than those without? To investigate, a group of Cal Poly students randomly sampled men from the obituaries page on the San Luis Obispo Tribunes webpage between June and November 2012. For each man selected, they noted the age at which
Reconsider the study mentioned in the previous exercise about an investigation of whether men with children tend to live longer, on average, than men without children.a. Define (in words) the parameters of interest of this study. Also, assign symbols to the parameters.b. Express the null and
Reconsider the study mentioned in the previous exercises about an investigation of whether men with children tend to live longer, on average, than men without children.The data are in the file ChildrenandLifespan. a. Use an appropriate randomization-based applet to fi nd a p-value to test
With randomization techniques we are able to analyze any statistic we desire. What if we wanted to look at whether the median lifespan of men with children was higher than men without children? Using the Multiple Means applet and the Median option on it, answer parts (a) through (f) of the previous
Rising mercury levels due to industrial pollution is a recent concern. Many fi sh have high levels of mercury. Data were collected on random samples of tuna from 1991 to 2010 and are available in the file Tuna. Each row in the data set represents the mercury level of a different fish. Do fresh
With randomization techniques we are able to analyze any test statistic we desire. What if we wanted to look at whether there was a difference in the median values of mercury in the Yellowfin tuna compared to the Albacore tuna? Using the Multiple Means applet and the Median option on it, answer
Recall Example 6.2 about the bike commuting times. On each of 56 days (from mid-January to mid-July 2010), researcher Jeremy Groves tossed a £1 coin to decide whether he would be biking the 27 miles to work on his carbon frame (lighter) bicycle that weighed 20.90 lb or on his steel frame
True or false, the parameter is fixed and unknown, while the statistic is the parameter plus a random error.
True or false, in a blind study, the subjects do not know which treatment they are receiving.
Read FAQ 6.2.2 and answer the following question: True or false, the statements “do not reject” and “accept” mean the same thing in a statistical conclusion.
Suppose that randomly sampled college students are asked how many hours they typically spend online each day. You conduct a two-sided test of the null hypothesis that μfemales − μmales = 0, and you also calculate a 95% confidence interval for μfemales − μmales.a. Describe (in words)
Reconsider Exercise 6.2.1 in which an instructor collected data on prices (in dollars) paid by students for their most recent haircut, also recording each student’s sex.A 95% confidence interval for μfemale − μmale turned out to be (12.17, 52.23). For each of the following, indicate
Reconsider the previous exercise about haircut prices. Suppose that the instructor wants to test whether females in the population paid more on average for their most recent haircut than males. Which kind of test might be appropriate? (Circle all that apply.)a. Simulation-based test comparing
Reconsider the previous exercise.a. Calculate a 95% confidence interval for the difference in population mean tip amounts between the two experimental treatments (giving name or not).b. Interpret what this interval means in this context.c. Is this confidence interval consistent with the test
Selvi et al. (2012) conducted a study on university medical students in Turkey to investigate whether and how sleep habits were associated with having nightmares. During the study, these students were engaged in lecture-based learning with no hospital duties. All participants were given initial
Reconsider the previous two exercises. How, if at all, would your analysis and conclusions change if the sample means had been closer together and all else had remained the same as in the original question? Be sure to refer to the test statistic, p-value, and confidence interval as well as give
Reconsider the previous exercise. How, if at all, would your analysis and conclusions change if the sample sizes had been larger and all else had remained the same? Be sure to refer to the test statistic, p-value, and confidence interval as well as give your conclusion.Data from previous
Reconsider the previous three exercises. How, if at all, would your analysis and conclusions change if the sample standard deviations had been larger and all else had remained the same as in the original question? Be sure to refer to the test statistic, p-value, and confidence interval as well as
Refer to the previous exercises. The researchers also gave each participant a score for Fear of sleeping because of anticipated nightmares. Given in the table below are the summary statistics for these scores. Note that higher scores indicate higher fear and that the data
Recall the study about anchoring from Exercise 6.2.16, in which students estimated the population of Milwaukee after some had been told about Chicago and others about Green Bay.a. Describe in words the parameter(s) of interest in the context of this study.b. In the context of the parameter(s)
In a study conducted in New Zealand, Parkin et al. randomly assigned volunteers to either wear socks over their shoes (intervention) or wear usual footwear (control) as they walked downhill on an inclined icy path. Researchers standing at the bottom of the inclined path measured the time (in
Left -right confusion (LRC) is the term used to describe the difficulty of distinguishing between left and right. In a study related to LRC, researchers Ocklenburg et al. (2011) gave a mental rotation test (MRT) to 91 neurologically healthy men and women. The MRT involved picking two images that
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
Do people tend to spend money differently based on perceived changes in wealth? In a study conducted by Epley et al. (2006), 47 Harvard undergraduates were randomly assigned to receive either a “bonus” check of $50 or a “rebate” check of $50. A week later, each student was contacted and
In an article titled Unilateral Nostril Breathing Influences Lateralized Cognitive Performance that appeared in Brain and Cognition (1989), researchers Block et al. published results from an experiment involving assessments of spatial and verbal cognition when breathing
Reconsider the previous exercise. In this question, we will focus on comparing 10 males who were randomly assigned to breathe only through their left nostril to 10 who were randomly assigned to breathe only through their right nostril while they took the spatial and verbal tests. Note: Ten of the
Reconsider the previous two exercises. In this question, we will focus on comparing 10 males who breathe only through their left nostril to 10 males who breathe only through their right nostril while they perform a verbal task. Assume that the verbal scores in each group are fairly symmetric.a.
Reconsider the data from Exercise 6.1.21 and corresponding statistics from Exercise 6.1.22 about drive-through times at two fast food restaurants. Conduct a two-sample t-test of whether the sample data provide strong evidence that the population mean drive-through times diff er between the two
Reconsider the previous exercise. Determine a 95% confidence interval for comparing the population mean drive-through times between the two fast food restaurants. Also interpret what this interval says. Finally, comment on whether the confidence interval is consistent with the conclusion of your
Reconsider the data from Exercise 6.1.23 about times spent in a public restroom by men and women in a Michigan mall. The average time in the bathroom was 106.65 (SD = 79.611) for the 40 men and 133.5 (SD = 62.369) for the 40 women. The data are not strongly skewed in either group. Conduct a
Reconsider the previous exercise. Determine a 95% confidence interval for comparing the population mean restroom times between the two sexes. Also interpret what this interval says. Finally, comment on whether the confidence interval is consistent with the conclusion of your significance test in
A psychology study (Rutchick, Slepian, and Ferris, 2010) investigated whether using a red pen causes people to assign lower scores than using a blue pen. A group of 128 students in an introductory undergraduate psychology class were asked to grade an eighth grader’s essay on a scale of 0–100.
Can waitresses increase their tips simply by introducing themselves by name when they greet customers? A waitress collected data on two-person parties that she waited on during Sunday brunch (with a fixed price of $23.21) at a Charley Brown’s restaurant in southern California. For each
As seen in Exploration 6.1, an instructor collected data on prices (in dollars) paid by students for their most recent haircut, also recording each student’s sex, to test whether females in the population paid more on average for their most recent haircut than males. Which of the following are
Read FAQ 6.1.2 and answer the following question: Which measure of spread is more resistant to outliers, SD or IQR?
Read FAQ 6.1.2 and answer the following question: True or false, a data point that is labeled an outlier is beyond 1.5 IQRs of either Q1 or Q3.
Read FAQ 6.1.2 and answer the following question: The IQR is calculated asA. Q1 − Q3 B. Mean − medianC. Min − max D. Q3 − Q1E. Median − mean F. Max − min
Read FAQ 6.1.1 and answer the following question:When should you use the median as a summary statistic instead of the mean?
You may have heard someone say that drinking coffee will stunt your growth. To test this, college students were asked their heights and if they were coffee drinkers. The data file CoffeeHeight.txt has the results. Copy and paste this data set into the Descriptive Statistics applet.a. Based on just
Statistics students found the sugar content of breakfast cereals, in grams per serving, for those placed on the high shelves of the store versus the low shelves. The data file CerealSugar.txt has these results. Copy and paste this data set into the Descriptive Statistics applet.a. If you want to
Reconsider the previous exercise where students responded to a survey where they were asked if they had ever been in a car crash while they were driving and how many minutes of exercise they had on the previous day. The data file CarCrashExercise.txt has these results. Copy and paste this data set
Statistics students were asked how many minutes of television they watched on the previous day. The results, in minutes, are shown in the 6.1.24 histograms, for the males in the top histogram and the females in the bottom histogram.a. In which direction is each distribution skewed?b. Will the mean
Students collect the time (in seconds) for men and women to use the restroom at a mall in Michigan. The results are shown in the 6.1.23 histograms.a. One data set (male or female) has both the larger mean and median. Which one is that?b. Do you think the median is larger, smaller, or about the same
Reconsider the drive-through times (in seconds) for a Wendys and a Hot n Now restaurant from the previous question.a. The means for the two sets of times are 93.70 and 203.00 seconds. Which belongs to which restaurant?b. The standard deviations for the two sets of times are
Students compared drive-through times at a couple of fast food restaurants in their town. They kept track of the time (in seconds) for people to go through the drive-through at Wendys*and Hot n Now*from the time of ordering until they exited the pick-up window during lunch
Using the candy bar weight data shown in the previous exercise, do the following:a. Find the five-number summary for both sets of candy bar weights.b. Construct parallel boxplots for both sets of candy bar weights.Data from previous exercise Mounds سني PayDay 24 22 2 20 23 19 21 Weight
Weights of 20 Mounds*candy bars and 20 PayDay*candy bars, in grams, are shown in the 6.1.19 dotplots.a. Describe how the distributions of weights of the two types of candy bars diff er in both variability and center.b. Based on your answers to part (a), which set of candy bar weights has the lowest
In a survey, 30 college students were asked what their usual bedtime was and the results are shown in the 6.1.18 dotplot in terms of hours aft er midnight. Negative responses are hours before midnight.a. Determine the five-number summary for the bed times.b. What is the inter-quartile range?c. The
The graph below displays the distribution of word lengths (number of letters) in the Gettysburg Address, which you explored in Exploration 2.1A.a. Describe the shape of this distribution.b. Based on this shape, do you expect the median to be less than the mean, greater than the mean, or very close
Reconsider the data in the previous question about number of hours spent studying.a. Find the median number of study hours for both males and females. What do these numbers tell us about the two data sets?b. Find the inter-quartile range for the number of study hours for both males and females.
In a survey of introductory statistics students, an instructor asked students to report how many hours they had spent studying in a typical week during the last term and their sex. The data appears in the 6.1.15 dotplot. Describe what the graph tells us about any similarities and differences
Reconsider the data in the dotplots from the previous question about average monthly temperatures for San Francisco and Raleigh.a. Determine the median temperature for each city. What do these numbers tell us about the two data sets?b. Determine the inter-quartile range for each city. What do these
The following dotplot shows the average monthly temperatures (oF) for San Francisco, CA, and Raleigh, NC.a. What are the observational units here?b. Identify the response variable and whether it is categorical or quantitative.c. Would the mean be a reasonable measure of center for these data? Why
Reconsider the data in the dotplot in the previous question about the number of states that students had visited. Suppose the observation recorded as 43 states is a typo and was meant to be 34. If we corrected this entry in the data set, how would the following numerical statistics change, if at
An instructor collected data on the number of states that 50 students in her class had visited in the U.S. The results are shown in the 6.1.11 dotplot.a. Use the dotplot to find and report the median value for the number of states visited by the students in this study.b. Use the dotplot to
A sample of heights (in inches) of 20 female statistics students is as follows:67, 64, 67, 65, 64, 65, 67, 64, 65, 60, 67, 67, 72, 65, 70, 63, 67, 65, 67, 70a. Find the median height.b. Find the first and third quartiles.c. Find the inter-quartile range.d. Construct a boxplot by hand for the data.
a. Suppose an instructor decides to add five points to every student’s exam score in a class. What effect would this have on the five-number summary? On the inter-quartile range? Explain.b. Suppose an instructor decides to add five points only to the exam score for the highest-scoring student in
The following set of scores was obtained from a quiz: 4, 5, 8, 9, 11, 13, 15, 18, 18, 18, 20. The teacher computes the usual descriptive measures of central tendency and spread for these data and then discovers that an error was made. One of the 18s should have been a 16. Which of the following
The following histogram is the distribution of the amount of time, in minutes, that some statistics students said they watched television the previous day. Using this graph to estimate the mean and median age for the amount of television watching time, we can conclude:A. The mean is smaller than
The following dotplot gives the ages of 21 male rattlesnakes. Which of the following would be true if one of the rattlesnakes whose age is given as 13 years is actually 15 and that change is made in the data set. (There may be more than one correct answer.)A. The median would increase.B. The mean
On a data set that is bell-shaped, which will typically be larger, its standard deviation or its inter-quartile range?
What are the five parts of the five-number summary?
Approximately what does the box portion of a boxplot display?A. The middle quarter of the dataB. The middle half of the dataC. The lower quarter of the dataD. The upper quarter of the data
Which of the following is NOT true about quartiles?A. The lower quartile is always smaller than the upper quartile.B. Quartiles can be calculated by determining the median of the values above/below the location of the overall median.C. Approximately 50% of the numbers in a data set lie between the
Which of the following is true about the interquartile range?A. It represents the range of approximately the middle quarter of a data set.B. It represents the range of approximately the middle 50% of a data set.C. If a value above the upper quartile is increased, the inter-quartile range will also
In the paper it states that “In this large, long-term trial of male physicians…vitamin C supplementation [did not] reduce the risk of major cardiovascular events. These data provide no support for the use of [vitamin C] for the prevention of cardiovascular disease in middle-aged and older
Later in the paper we find out that 619 out of 7,329 men who got Vitamin C had a “major cardiovascular event” compared to 626 out of 7,312 men who got the placebo. We also read that the p-value for a difference in incidence rates is 0.91. Find the incidence rates, state the null and alternative
Explain what it means for the Physicians’ Health Study II to be….a. …randomized.b. …double-blind.c. …placebo-controlled.The Physicians’ Health Study II was a randomized, double-blind, placebo- controlled … trial of … vitamin C that began in 1997 and continued until its scheduled
Summarize your findings from the study. What did you like about the study design? What would you change to improve the study? What further research might you want to do to follow up or expand upon the results in this study?
Can we make a cause-and-effect conclusion? Why or why not?
Can we generalize our conclusion to the entire human population? What should be true of the 279 skiers in order for your conclusion to be drawn to the entire human population? Discuss how the sample was obtained. Are there characteristics about the sample subjects that make this an unreasonable
Find the p-value of your test. Is this strong enough evidence for you to conclude that Vitamin C prevented colds in the skiers? Write a sentence stating your conclusion as it applies to the question. Remember to use words pertaining to the research question.
What is the shape of your null distribution and where is its center located? Why does it make sense for the center to be located where it is?
When you shuffle, you are simulating one of the two hypotheses (null or alternative) to be true: Which one are you simulating?
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 conjecture that Vitamin C prevents colds.
Reconsider the previous exercise. The same survey found that 65% of women and 50% of men would give CPR to their pets. Answer parts (a) to (c) from the previous exercise for these data.Data from previous exercisea. Produce a well-labeled segmented bar graph to display these percentages.b. Identify
According to a survey conducted by the Associated Press and petside.com in 2009, 63% of dog owners and 53% of cat owners would be at least somewhat likely to give CPR to their pet in the event of a medical emergency. The survey involved a nationwide sample of 1,166 pet owners.a. Produce a
In a 1994 study, 164 pregnant, HIV-positive women were randomly assigned to receive the drug AZT during pregnancy and 160 such women were randomly assigned to a control group that received a placebo. It turned out that 40 of the mothers in the control group gave birth to babies who were
Reconsider the previous exercise. The Pew study also considered age as an explanatory variable, producing the following 2 Ã 2 table of counts:Analyze these data with appropriate numerical summaries and graphical displays. Write a paragraph summarizing what you learn about whether there
A Pew Research study in April and May of 2013 asked single American adults whether they have ever broken up with someone by e-mail, text, or online message. Consider the following 2 Ã 2 table of counts:a. Notice that there are more males (55) than females (52) who have broken up with
Reconsider the previous exercise.a. Calculate the relative risk of being a smoker, comparing those who never attend church to those who attend church at least once per week. Also write a sentence interpreting what this calculation reveals.b. Repeat (a) for the other three categories of church
A Gallup poll conducted in 2013 examined whether there is an association between church attendance and smoking status among American adults. The following table reports the percentage of people who classify themselves as smokers, conditional on self-described level of church attendance.a. Is this
Reconsider the previous three exercises, but now ignore the real data. Invent your own fictional data that show no association between party and sex of senator. Provide the 2 × 2 table, calculate conditional proportions, and produce a segmented bar graph. Also explain how you invented the data to
Reconsider the previous two exercises.a. Produce a well-labeled segmented bar graph to display the association between party and sex of senator.b. Does the graph reveal that there is an association between party and sex of senator in the 2014 U.S. Senate? If so, describe the association.Data from
Reconsider the previous exercise, along with this additional information: 16 senators are women Democrats.a. Produce a 2 × 2 table that classifies senators in the 2014 U.S. Senate according to party and sex of senator. Provide the relevant proportion(s) to answer the following questions:b. Are
The 2014 U.S. Senate consists of 80 men and 20 women. Th e 2014 U.S. Senate consists of 45 Republicans and 55 Democrats (counting 2 Independents as Democrats because they vote with Democrats more than with Republicans). What additional information do you need in order to produce a 2 × 2 table and
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