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theory of statistics
Statistics For The Behavioral Sciences 5th Edition Susan A Nolan, Thomas Heinzen - Solutions
Null hypotheses and research hypotheses: For each of the following studies, cite the likely null hypothesis and the likely research hypothesis.
Independent or dependent trials and probability:Gamblers oen falsely predict the outcome of a future trial based on the outcome of previous trials. When trials are independent, the outcome of a future trial cannot be predicted based on the outcomes of previous trials. For each of the following
Independent trials and the U.S. presidential election:Nate Silver is a statistician and journalist who uses statistics to create prediction tools. In an article leading up to the 2012 U.S.presidential election in which Barack Obama bested Mitt Romney, Silver (2012) explained his prediction methods
Independent trials and Eurovision Song Contest bias: As reported in the Telegraph (Higheld, 2005), Oxford University researchers investigated allegations of voting bias in the annual Eurovision Song Contest, which pits pop music acts from across Europe, one per country, against each other. The
Probability, proportion, percentage, and Where’s Waldo?:Slate.com reporter Ben Blatt (2013) analyzed the location of Waldo in the game in which you must nd Waldo, a cartoon man who always wears a red-and-white-striped sweater and hat, in a highly detailed illustration. Blatt reported that “53
Probability and coin ips: Short-run proportions are oen quite different from long-run probabilities.a. In your own words, explain why we would expect proportions to uctuate in the short run, but why longrun probabilities are more predictable.b. What is the expected long-run probability of heads if
Conrmation bias and negative thought patterns: Explain how the general tendency of a conrmation bias might make it difcult to change negative thought patterns that accompany major depressive disorder.
Random sampling or random assignment: For each of the following hypothetical scenarios, state whether sampling or assignment is being described. Is the method of sampling or assignment random? Explain your answer.a. A study of the services offered by counseling centers at Canadian universities
Samples and a survey on sex education: The Gizmodo blog Throb, a Web site focused on the science of sex, released its own sex education survey (Kelly, 2015). The journalist who developed the survey wrote: “I hope that with enough of your answers, we can start to build a picture of what sex ed
Samples and Cosmo quizzes: Cosmopolitan magazine(Cosmo, as it’s known popularly) publishes many of its wellknown quizzes on its Web site. One quiz, aimed at heterosexual women, is titled “Are You Way Too Obsessed with Your Ex?” A question about “your rebound guy” offers these three
Online sampling and visualizing neurons: Researcher Zoran Popović has developed a video game called Mozak (SerboCroatian for “brain”) for the Allen Institute for Brain Science that enlists players—research participants, actually—to trace lines over images of neurons (Wingeld, 2017). The
Random sampling and random assignment: For each of the following studies, state (1) whether random sampling was likely to have been used, and explain whether it would have been possible to use it. Also, describe the population to which the researcher wanted to and could generalize, and state (2)
Random sampling and a survey of psychology majors:Imagine that you have been hired by the psychology department at your school to administer a survey to psychology majors about their experiences in the department. You have been asked to randomly select 60 of these majors from the overall pool of
Negativity bias and WEIRD: Refer to the description of the study by Amber Boydstun and her colleagues (2019) in the previous exercise. How is the COG statement provided by the authors related to the WEIRD problem?
Negativity bias and constraints on generality: In a recent article, Amber Boydstun and her colleagues (2019) described a study on the effects of negativity bias in a political context. Negativity bias is the nding that people’s decisions are more inuenced by negatively framed information (e.g.,
Random assignment and the school psychologist career survey: Refer to the previous exercise when responding to the following questions.a. Describe how the researcher would randomly assign the participants to the levels of the independent variable.
Hypotheses and the school psychologist career survey:Continuing with the study described in the previous exercise, once the researcher had randomly selected the sample of 100 Canadian psychologists, she decided to randomly assign 50 of them to receive, as part of their survey materials, a
Random sampling and a school psychologist career survey: Imagine that the Canadian government reported that there are 7550 psychologists working in Canada. A researcher wants to randomly sample 100 of the Canadian psychologists for a survey study regarding aspects of their jobs.a. What is the
Random numbers and PINs: How random is your personal identication number or PIN? Your PIN is one of the most important safeguards for the accounts that hold your money and valuable information about you. The BBC reported that, when choosing a four-digit PIN,“people dri towards a small subset of
Coincidence and the lottery: “Woman wins millions from Texas lottery for 4th time” read the headline about Joan Ginther’s amazing luck (Wetenhall, 2010). Two of the tickets were from the same store, whose owner, Bob Solis, said,“This is a very lucky store.” Citing concepts from the
Indicate whether each of the following statements refers to personal probability or to expected relative-frequency probability. Explain your answers.
Convert the following percentages to proportions:
Convert the following percentages to proportions:a. 62.7%b. 0.3%c. 4.2%
Convert the following proportions to percentages:a. 0.0173b. 0.8c. 0.3719
On a game show, 8 people have won the grand prize and a total of 266 people have competed. Estimate the probability of winning the grand prize.
What is the probability of hitting a target if, in the long run, 71 out of every 489 attempts actually hit the target?
Explain why, given the general tendency people have of perceiving illusory correlations, it is important to collect objective data.
Explain why, given the general tendency people have of exhibiting the conrmation bias, it is important to collect objective data.
You are running a study with ve conditions, numbered 1 through 5. Using an online random numbers generator, assign the rst seven participants who arrive at your lab to conditions, not worrying about equal assignment across conditions.
Randomly assign eight people to three conditions of a study, numbered 1, 2, and 3 using an online random numbers generator. (Note: Assign people to conditions without concern for having an equal number of people in each condition.)
Airport security makes random checks of passenger bags every day. If 1 in every 10 passengers is checked, use an online random numbers generator to determine the rst 6 people to be checked—that is, which one of the rst 10 people, which one of the second set of 10 people, and so on?
Forty-three tractor-trailers are parked for the night in a rest stop along a major highway. You assign each truck a number from 1 to 43. Use an online random numbers generator to select four trucks to weigh as they leave the rest stop in the morning.
What is the difference between a Type I error and a Type II error?
What are the two decisions or conclusions we can make about our hypotheses, based on the data?
What is the difference between a null hypothesis and a research hypothesis?
One step in hypothesis testing is to randomly assign some members of the sample to the control group and some to the experimental group. What is the difference between these two groups?
What are the ways the term independent is used by statisticians?
We distinguish between probabilities and proportions.How does each capture the likelihood of an outcome?
Statisticians use terms like trial, outcome, and success in a particular way in reference to probability. What do each of these three terms mean in the context of ipping a coin?
In your own words, what is expected relative-frequency probability?
In your own words, what is personal probability?
How does the conrmation bias lead to the perpetuation of an illusory correlation?
What is an illusory correlation?
What is the conrmation bias?
Ideally, an experiment would use random sampling so that the data would accurately reect the larger population. For practical reasons, this is difcult to do. How does random assignment help make up for a lack of random sampling?
What does it mean to replicate research, and how does replication affect our condence in the ndings?
What is the difference between random sampling and random assignment?
What is a constraints on generality (COG) statement?
What does WEIRD stand for, and what is the problem that led to the coining of this term?
What are some of the pros and cons of crowdsourced data?
What is crowdsourcing in research?
What is a volunteer sample, and what is the main risk associated with it?
What is generalizability?
What is the difference between a random sample and a convenience sample?
Why do we study samples rather than populations?
Central tendency and outliers for data on trafc deaths: Below are estimated numbers of annual road trafc deaths for 12 countries based on data from the World Health Organization (apps.who.int/gho/data/view.main.51310):
Descriptive statistics and basketball wins: Here are the numbers of wins for the 30 National Basketball Association teams in one season.
Range, world records, and a long chain of friendship bracelets: Guinness World Records reported that, as part of an anti-bullying campaign, elementary school students in Pennsylvania created a chain of friendship bracelets that was a world-record 2678 feet
Standard deviation and a texting intervention for parents of preschoolers:Researchers investigated READY4K, a program in which parents received text messages over an 8-month period (York & Loeb, 2014). The goal of the text messages was to help parents prepare their preschool-aged children for
Median ages and technology companies: In an article titled “Technology Workers Are Young (Really Young),” The New York Times reported median ages for a number of companies(Hardy, 2013). The reporter wrote: “The seven companies with the youngest workers, ranked from youngest to highest in
Mean versus median for age at rst marriage: The mean age at rst marriage was 31.1 years for men and 29.1 years for women in Canada in 2008 (open.canada.ca/en/open-data).The median age at rst marriage was 28.9 years for men and 26.9 years for women in the United States in 2011
Teaching assistants, race, and standard deviations: Researchers reported that the race of the teaching assistants (TAs) for a class had an effect on student outcome (Lusher et al., 2015). They reported that “Asian students receive a 2.3% of a standard deviation increase in course grade when the
Central tendency and outliers from growth-chart data: When the average height or average weight of children is plotted to create growth charts, do you think it would be appropriate to use the mean for these data? There are oen outliers for height, but why might we not have to be concerned with
Outliers, H&M, and designer collaborations: The relatively low-cost Swedish fashion retailer H&M occasionally partners with high-end designers. For example, it collaborated with the Italian designer brand Moschino, and the line quickly sold out. If H&M were to report the average number of sales per
Outliers, Hurricane Sandy, and a rat infestation: In a New York Times article, reporter Cara Buckley (2013) described the inux of rats inland from the New York City shoreline following the ooding caused by Hurricane Sandy. Buckley interviewed pest-control expert Timothy Wong, who noted that rat
Shapes of distributions, chemistry grades, and rst-generation college students:David Laude was a chemistry professor at the University of Texas at Austin (and a former underprepared college student) who developed an intervention that led underprepared
Central tendency and the shapes of distributions: Consider the many possible distributions of grades on a quiz in a statistics class; imagine that the grades could range from 0 to 100. For each of the following situations, give a hypothetical mean and median(i.e., make up a mean and a median that
Statistics versus parameters: For each of the following situations, state whether the mean or median would be a statistic or a parameter. Explain your answer.a. According to Canadian census data, the median family income in British Columbia was $66,970, lower than the national median of $69,860.b.
Descriptive statistics for data from the National Survey of Student Engagement:Every year, the National Survey of Student Engagement (NSSE) asks U.S. university students how many 20-page papers they had been assigned. Here are the percentages, for 1 year, of students who said they had been assigned
Range of data for Canadian TV ratings: Numeris (formerly BBM Canada) collects Canadian television ratings data (en.numeris.ca). The following are the average number of viewers per minute (in thousands) for the top 30 English-language shows for 1 week. The NHL playoffs are listed at 1198, which
Descriptive statistics in the media: When there is an ad on TV for a body-shaping product (e.g., an abdominal muscle machine), oen a person with a wonderful success story is featured in the ad. The statement “Individual results may vary” hints at what kind of data the advertisement may be
Descriptive statistics in the media: Find an advertisement for an anti-aging product either online or in the print media—the more unbelievable the claims, the better!a. What does the ad promise that this product will do for the consumer?b. What data does it offer for its promised benets? Does it
Mean versus median in “real life”: Briey describe a real-life situation in which the median is preferable to the mean. Give hypothetical numbers for the mean and median in your explanation. Be original! (Don’t use home prices or another example from the chapter.)
Measures of central tendency for measures of baseball performance: Here are winning percentages for 11 baseball players for their best 4-year pitching performances: 0.755 0.721 0.708 0.773 0.78 0.747 0.477 0.817 0.617 0.650 0.651a. What is the mean of these scores?b. What is the median of these
Outliers, central tendency, and data on wind gusts: There appears to be an outlier in the data for peak wind gust recorded on top of Mount Washington (see the data in Exercise 4.19). Where do you see an outlier and how does excluding this data point affect the different calculations of central
Measures of central tendency for weather data: The “normal” weather data from the Mount Washington Observatory are broken down by month. Why might you not want to average across all months in a year? How else could you summarize the year?
Mean versus median for depression scores: A depression research unit recently assessed seven participants chosen at random from the university population. Is the mean or the median a better indicator of the central tendency of these seven participants? Explain your answer.
Mean versus median for temperature data: For the data in Exercise 4.19, the “normal”daily maximum and minimum temperatures recorded at the Mount Washington Observatory are presented for each month. These are likely to be measures of central tendency for each month over time. Explain why these
and 4.18, we saw how the mean and median changed when an outlier was included in the computations. If you were reporting the “average” salary at a company, how might the mean and the median give different impressions to potential applicants?
Mean versus median for salary data: In Exercises
Here are recent U.S. News & World Report data on acceptance rates at the top 70 national universities. These are the percentages of accepted students out of all students who applied.
Why is the interquartile range you calculated for the previous exercise so much smaller than the range you calculated in Exercise 4.19?
Using the data presented in Exercise 4.19, calculate the interquartile range for peak wind gust.
Calculate the interquartile range for the following set of data:2 5 1 3 3 4 3 6 7 1 4 3 7 2 2 2 8 3 3 12 1
Calculate the range and the interquartile range for the following set of data. Explain why they are so different.83 99 103 65 66 77 55 82 93 93 108 543 72 109 115 85 92 74 101 98 84
The Mount Washington Observatory (MWO) in New Hampshire claims to have the world’s worst weather. Below are some data on the weather extremes recorded at the MWO.
Use the following salary data for this exercise:$44,751 $38,862$52,000 $51,380$41,500 $61,774a. Calculate the mean, the median, and the mode.b. Add another salary, $97,582. Calculate the mean, median, and mode again. How does this new salary affect the calculations?c. Calculate the range, variance,
Use the following data for this exercise:15 34 32 46 22 36 34 28 52 28a. Calculate the mean, the median, and the mode.b. Add another data point, 112. Calculate the mean, median, and mode again. How does this new data point affect the calculations?
Find the incorrectly used symbol or symbols in each of the following statements or formulas. For each statement or formula, (1) state which symbol(s) is/are used incorrectly,(2) explain why the symbol(s) in the original statement is/are incorrect, and (3) state which symbol(s) should be used.a. The
Why is the standard deviation typically reported, rather than the variance?
Dene the symbols used in the equation for variance:
Explain the concept of standard deviation in your own words.
At what percentile is the third quartile?
At what percentile is the rst quartile?
Using your knowledge of how to calculate the median, describe how to calculate the rst and third quartiles of your data.
How does the interquartile range differ from the range?
In which situations is the mode typically used?
How do outliers affect the mean and the median?
What is an outlier?
Explain why the mean might not be useful for a bimodal or multimodal distribution.
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