Questions and Answers of Essentials of Statistics

From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 4 pieces of fruit is selected. If X is the number of oranges and Y is the number of apples in the sample,
If the joint probability distribution of X and Y is given byfor x = 0, 1, 2, 3; y = 0, 1, 2,find(a) P(X ‰¤ 2, Y = 1);(b) P(X >2, Y ‰¤ 1);(c) P(X >Y);(d) P(X + Y = 4).(e)
Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete
Consider the density function(a) Evaluate k.(b) Find F(x) and use it to evaluate P(0.3 < X < 0.6). (kVT, 0
An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of T, the number of years to maturity for a
An industrial plant is conducting a study to determine how quickly injured workers are back on the job following injury. Records show that 10% of all injured workers are admitted to the hospital for
Denote by A, B, and C the events that a grand prize is behind doors A, B, and C, respectively. Suppose you randomly picked a door, say A. The game host opened a door, say B, and showed there was no
Pollution of the rivers in the United States has been a problem for many years. Consider the following events: A: the river is polluted, B: a sample of water tested detects pollution, C: ﬁshing is
If R is the event that a convict committed armed robbery and D is the event that the convict sold drugs, state in words what probabilities are expressed by(a) P(R|D);(b) P(D'|R);(c) P(R'|D').
Prove that P(A'∩B') = 1 + P(A∩B) − P(A) − P(B).
Interest centers around the nature of an oven purchased at a particular department store. It can be either a gas or an electric oven. Consider the decisions made by six distinct customers.(a) Suppose
Factory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur because the working environment or conditions themselves are unsafe.
Referring to Exercise 1.15 and the Venn diagram of Figure 1.7, list the numbers of the regions that represent the following events:Fig 1.7(a) The family will experience no mechanical problems and
Two jurors are selected from 4 alternates to serve at a murder trial. Using the notation A1A3, for example, to denote the simple event that alternates 1 and 3 are selected, list the 6 elements of the
List the elements of each of the following sample spaces:(a) The set of integers between 1 and 50 divisible by 8;(b) The set S = {x | x2 +4x−5=0 };(c) The set of outcomes when a coin is tossed
The previous exercise describes a study conducted by Busseri and colleagues (2009) using a group of pessimists. These researchers asked the same question of a group of optimists: Optimists rated
Researchers Busseri, Choma, and Sadava (2009) asked a sample of individuals who scored as pessimists on a measure of life orientation about past, present, and projected future satisfaction with their
Commercials for chewing gum make claims about how long the flavor will last. In fact, some commercials claim that the flavor lasts too long, affecting sales and profit. Let€™s put these
Imagine a researcher wanted to assess people€™s fear of dogs as a function of the size of the dog. He assessed fear among people who indicated they were afraid of dogs, using a 30-point
Researchers Raluca Barac and Ellen Bialystok (2012) conducted a study in which they compared the language skills of 104 six-year-old children who were in one of four groups. Some children spoke only
Two samples of students, one comprised of social science majors and one comprised of students with other majors, completed the Consideration of Future Consequences scale (CFC). The accompanying
Researchers asked 180 U.S. students to identify their political viewpoint as most similar to that of the Republicans, most similar to that of the Democrats, or neither. All three groups then
For the following data, assuming a within-groups design, determine:a. dfbetween = Ngroups ˆ’ 1b. dfsubjects = n ˆ’ 1c. dfwithin = (dfbetween)(dfsubjects)d. dftotal = dfbetween +
For the following data, assuming a within-groups design, determine:a. dfbetween = Ngroups ˆ’ 1b. dfsubjects = n ˆ’ 1c. dfwithin = (dfbetween)(dfsubjects)d. dftotal = dfbetween +
Researchers studied the effects of learning about the effectiveness of a new medication (Tal & Wansink, 2014). Some participants heard information about the medication; others heard the same
Kiho Kim and Stevia Morawski (2012) reported the following in the abstract (brief summary) of their published research study: “Here, we report on the results of an experiment to evaluate the
Volkswagen has created a series of videos based on its “fun theory,” the idea that you can change behavior if you take an activity that is good for society and makeit fun. (You can watch the
Using the research studies described in the previous exercise, create null hypotheses and research hypotheses appropriate for the chosen statistical test:a. Taylor and Ste-Marie (2001) studied eating
Some people claim that women can experience “mother hearing,” an increased sensitivity to and awareness of noises, in particular those of children. This special ability is often associated with
At some vacation destinations, “all-inclusive” resorts allow you to pay a flat rate and then eat and drink as much as you want. There has been concern about whether these deals might lead to
Are Women Really More Talkative Than Men?€ is the title of an article that appeared in the journal Science. In the article, Mehl, Vazire, Ramirez- Esparza, Slatcher, & Pennebaker
In an example we sometimes use in our statistics classes, several semesters€™ worth of male and female students were asked how long, in minutes, they spend getting ready for a date. The
Iranian researchers studied factors affecting patients’ likelihood of wearing orthodontic appliances, noting that orthodontics is perhaps the area of health care with the highest need for patient
In Chapter 10, we introduced a study by Steele and Pinto (2006) that examined whether people’s level of trust in their direct supervisor was related to their level of agreement with a policy
Pilots’ mental efforts and a one-way withingroups ANOVA: Researchers examined the amount of mental effort that participants felt they were expending on a cognitively complex task, piloting an
Catherine Ruby, a doctoral student at New York University, conducted an online survey to ascertain the reasons that international students chose to attend graduate school in the United States. One of
For each of the following situations, state whether the distribution of interest is a z distribution, a t distribution, or an F distribution. Explain your answer.a. A city employee locates a U.S.
Focusing on coverage of the U.S. presidential election, Julia R. Fox, a telecommunications professor at Indiana University, wondered whether The Daily Show, despite its comedy format, was a valid
Stacey Finkelstein and Ayelet Fishbach (2012) examined the impact of feedback in the learning process. The following is an excerpt from their abstract: €œThis article explores what feedback
What magnitude of a correlation coefficient is large enough to be considered important, or worth talking about?
When we have a straight-line relation between two variables, we use a Pearson correlation coefficient. What does this coefficient describe?
Explain how the correlation coefficient can be used as a descriptive or an inferential statistic.
Using the following data:a. Create a scatterplot.b. Calculate deviation scores and products of the deviations for each individual, and then sum all products. This is the numerator of the correlation
The following figures display data that depict the relation between students' monthly cell phone bills and the number of hours they report that they study per week.a. What does the accompanying
In a classic prisoner€™s dilemma game with money for prizes, players who cooperate with each other both earn good prizes. If, however, your opposing player cooperates but you do not (the
Calculate the F statistic, writing the ratio accurately, for each of the following cases:a. Between-groups variance is 29.4 and within-groups variance is 19.1b. Within-groups variance is 0.27 and
For the following data, assuming a between-groups design, determine:a. dfbetweenb. dfwithinc. dftotald. The critical value, assuming a p value of 0.05e. The mean for each group and the grand meanf.
Why is it appropriate to counterbalance when using a within-groups design?
What is counterbalancing?
What is the advantage of the design of the within-groups ANOVA over that of the between-groups ANOVA?
Explain the source of variability called “subjects.”
What are order effects?
What are the four assumptions for a within-groups ANOVA?
Find the incorrectly used symbol or symbols in each of the following statements or formulas. For each statement or formula, (i) state which symbol(s) is/are used incorrectly, (ii) explain why the
Find the error in the statistics language in each of the following statements about z, t, or F distributions or their related tests. Explain why it is incorrect and provide the correct word.a. The
Researchers at the Cornell University Food and Brand Lab conducted an experiment at a fitness camp for adolescents (Wansink & van Ittersum, 2003). Campers were given either a 22-ounce glass that
Alice Waters, owner of the Berkeley, California, restaurant Chez Panisse, has long been an advocate for the use of simple, fresh, organic ingredients in home and restaurant cooking. She has also
Chang, Sandhofer, and Brown (2011) wondered whether mothers used number words more, on average, with their preschool sons than with their preschool daughters. Each participating family included one
For the following data, assuming a between-groups design, determine:a. dfbetweenb. dfwithinc. dftotald. The critical value, assuming a p value of 0.05e. The mean for each group and the grand meanf.
Researchers explored whether there were mean differences between students who were randomly assigned to take notes longhand and students who were randomly assigned to take notes on their laptops
Identify the critical t values for each of the following tests:a. A single-sample t test examining scores for 26 participants to see if there is any difference compared to the population, using a p
Unsavory researchers know that one can cheat with hypothesis testing. That is, they know that a researcher can stack the deck in her or his favor, making it easier to reject the null hypothesis.a. If
In an exercise in Chapter 7, we asked you to conduct a z test to ascertain whether the Graded Naming Test (GNT) scores for Canadian participants differed from the GNT norms based on adults in
In your own words, define the word effect—first as you would use it in everyday conversation and then as a statistician would use it.
Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test,
Hurricane Katrina hit New Orleans on August 29, 2005. The National Weather Service Forecast Office maintains online archives of climate data for all U.S. cities and areas. These archives allow us to
For each of the following examples (the same as those in Exercise 7.41), state the null hypothesis and the research hypothesis, in both words and symbolic notation:a. A researcher is interested in
For each of the following examples, identify whether the research has expressed a directional or a nondirectional hypothesis:a. A researcher is interested in studying the relation between the use of
What is the difference between parametric tests and non-parametric tests?
What is a percentile?
The General Social Survey (GSS) is a survey of approximately 2000 adults conducted each year since 1972, for a total of more than 38,000 participants. During several years of the GSS, participants
See the description of the MMPI-2 in Exercise 6.47. The mean T score is always 50, and the standard deviation is always 10. Imagine that you administer the MMPI-2 to 50 respondents who do not use
A sample of 100 people had a mean depression score of 85; the population mean for this depression measure is 80, with a standard deviation of 20. A different sample of 100 people had a mean score of
Compute a z statistic for each of the following, assuming the population has a mean of 100 and a standard deviation of 20:a. A sample of 43 scores has a mean of 101.b. A sample of 60 scores has a
A population has a mean of 55 and a standard deviation of 8. Compute μM and σM for each of the following sample sizes:a. 30b. 300c. 3000
Assume a normal distribution when answering the following questions.a. What percentage of scores falls below the mean?b. What percentage of scores falls between 1 standard deviation below the mean
Compare the following scores:a. A score of 811 when μ = 800 and σ = 29 against a score of 4524 when μ = 3127 and σ = 951b. A score of 17 when μ = 30 and σ = 12 against a score of 67 when μ =
Using the instructions in Example 6.8, compare the following “apples and oranges”: a score of 45 when the population mean is 51 and the standard deviation is 4, and a score of 732 when the
A study of the Consideration of Future Consequences (CFC) scale found a mean score of 3.20, with a standard deviation of 0.70, for the 800 students in the sample (Adams, 2012). (Treat this sample as
For a population with a mean of 1179 and a standard deviation of 164, convert each of the following z scores to raw scores.a. −0.23b. 1.41c. 2.06d. 0.03
For a population with a mean of 250 and a standard deviation of 47, convert each of the following z scores to raw scores.a. 0.54b. −2.66c. −1.00d. 1.79
Create a histogram for these three sets of scores. Each set of scores represents a sample taken from the same population.a. 6 4 11 7 7b. 6 4 11 7 7 2 10 7 8 6 6 7 5 8c.d. What do you observe
What is the difference between a null hypothesis and a research hypothesis?
A population has a mean of 250 and a standard deviation of 47. Calculate z scores for each of the following raw scores:a. 391b. 273c. 199d. 160
Report the following numbers to two decimal places: 0.0391; 198.2219; and 17.886.
What is the difference between reliability and validity, and how are the two concepts related?
What is the relation between an independent variable and a dependent variable?
In the fall of 2008, the U.S. stock market plummeted several times, with grave consequences for the world economy. A researcher might assess the economic effect this situation had by seeing how much
The following statements are wrong but can be corrected by substituting one word or phrase. (See the instructions in Exercise 1.13.) Identify the incorrect word or phrase in each of the following
A researcher interested in the cultural values of individualistic and collectivist societies collects data on the rate of relationship conflict experienced by 32 people who test high for
For decades, researchers, politicians, and tobacco company executives debated the relation between smoking and health problems such as cancer.a. Why was this research necessarily correlational in
Noting marked increases in weight across the population, researchers, nutritionists, and physicians have struggled to find ways to stem the tide of obesity in many Western countries. They have
In 2013, Forbes reported the 10 top-earning comedians, and all 10 were men—Louis C.K., Kevin Hart, and Larry the Cable Guy among them. A number of online journalists wanted to know why there were
A study on motivated skepticism examined whether participants were more likely to be skeptical when it served their self-interest (Ditto & Lopez, 1992). Ninety-three participants completed a
German psychologist David Loschelder and his colleagues conducted an experiment on negotiations (2014). They cited tennis player Andy Roddick€™s agent who thought it was always detrimental
Heyman and Ariely (2004) were interested in whether effort and willingness to help were affected by the form and amount of payment offered in return for effort. They predicted that when money was
The data below were from the same 25-yearold participants described in How It Works 12.1, but now the scores represent the oldest age that would be acceptable in a dating partner.25-year-old women
A sample of students from our statistics classes reported their GPAs, indicated their genders, and stated whether they were in the university’s Greek system (i.e., in a fraternity or sorority).
Hugenberg, Miller, and Claypool (2007) conducted a study to better understand the cross-race effect, in which people have a difficult time recognizing members of different racial
Eleanor Barkhorn (2012) reported in the Atlantic about differences in women’s and men’s negotiating styles. She first explained that researchers did not find a significant difference in how

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