Statistics For Economics Accounting And Business Studies 7th Edition Michael Barrow - Solutions

Discover comprehensive solutions for "Statistics For Economics Accounting And Business Studies 7th Edition" by Michael Barrow with our online resources. Access a complete answers key, solution manual, and solutions PDF that include solved problems and step-by-step answers. Our offerings include a test bank and chapter solutions, providing a thorough guide through the textbook. Whether you're looking for questions and answers or an instructor manual, our free download options make it easy to enhance your understanding and performance. Get the most out of your textbook with these valuable resources available online.

What are the steps to create a frequency table?
What are raw scores?
Assessing charitable organizations: Many people do research on charitable organizations before deciding where to donate their money. Tina Rosenberg (2012) reported that traditionally many people have used sources such as Charity Navigator or the Better Business Bureau’s Web sites. Both of these
Ability and wages: Arcidiacono, Bayer, and Hizmo (2008)analyzed data from a national longitudinal survey called NLSY79, which includes data from more than 12,000 men and women in the United States who were in the 14- to 22-year age range in 1979. The researchers reported that ability is related to
Experiments, HIV, and cholera: Several studies have documented that people who are HIV-positive are susceptible to cholera (likely because of having a weakened immune system).Researchers in Mozambique (Lucas et al., 2005), a country where an estimated 20% to 30% of the population is HIVpositive,
Romantic relationships: Goodman and Greaves (2010)reported ndings from the Millennium Cohort Study, a large research project in the United Kingdom. They stated that “while it is true that cohabiting parents are more likely to split up than married ones, there is very little evidence to suggest
HARKing, a Texas sharpshooter, and preregistration:Australian psychologist Mark Rubin (2017) likened the unethical practice of HARKing to the tale of the Texas sharpshooter.Rubin explains that the sharpshooter “aims and res his gun at[a] target on a barn wall but misses. He then walks up to the
Data ethics and “eat your peas”: The New York Times reporter Anahad O’Connor (2018) reported on a scandal in the eld of psychology. A well-known researcher of food-related behaviors, Brian Wansink, resigned from his position at Cornell University aer university investigators discovered
Experimental versus correlational research and recycling: A study in Argentina concluded that grocery store customers were more likely to bring their own bags when stores charged for plastic bags than when stores did not charge(Jakovcevic et al., 2014). Imagine that you want to design a follow-up
Experimental versus correlational research and culture:A researcher interested in the cultural values of individualistic and collectivist societies collects data on the rate of relationship conict experienced by 32 people who test high for individualism and 37 people who test high for collectivism?
Correlational research and vaping: As the use of ecigarettes, or vaping, becomes more popular, researchers are realizing the potential negative effects of this behavior.According to Scientic American (2018), researchers have investigated the harmful effects of nicotine, including its links to heart
Between-groups versus within-groups and exercise:Noting marked increases in weight across the population, researchers, nutritionists, and physicians have struggled to nd ways to stem the tide of obesity in many Western countries.They have advocated a number of exercise programs, and there has been
Operationalizing the earnings of comedians: In 2013, Forbes reported the 10 top-earning comedians, and all 10 were men—Daniel Tosh, Kevin Hart, and Larry the Cable Guy among them. A number of online journalists wanted to know why there were no women on the list. Erin Gloria Ryan of Jezebel, for
Operationalizing variables and rap statistics: A few years back, the Web site Rap Genius (now just Genius) analyzes rap music using what it calls RapMetrics (rapgenius.com/posts/63-Introducing-rapmetricstm-the-birth-of-statistical-analysis-ofrap-lyrics). It developed a measure called rhyme density,
Reliability, validity, and wine ratings: You may have been in a wine store and wondered just how useful those posted wine ratings are. (They are usually rated on a scale from 50 to 100, with 100 being the top score.) Aer all, aren’t ratings subjective?Corsi and Ashenfelter (2019) studied whether
Reliability and validity: Go online and take the personality test found at outofservice.com/starwars. This test assesses your personality in terms of the characters from the original Star Wars movies.a. What does it mean for a test to be reliable? Take the test a second time. Does it seem to be
Discrete versus continuous variables: For each of the following examples, state whether the scale variable is discrete or continuous.a. The capacity, in terms of songs, of a smartphoneb. The playing time of an individual songc. The cost to download a song legally
Types of variables and the Kentucky Derby: The Kentucky Derby is perhaps the premier event in U.S. horse racing. For each of the following examples from the derby, identify the type of variable—nominal, ordinal, or scale.a. As racing fans, we would be very interested in the variable nishing
seconds, and le Clos and Korotyshkin nished in 51.44 seconds.c. Phelps and Korotyshkin live in the Northern Hemisphere, whereas le Clos lives in the Southern Hemisphere.
Types of variables and Olympic swimming: At the 2012 London Summer Olympics, American Michael Phelps won 4 gold medals, bringing his overall Olympic career total to 18 gold medals, the all-time career record for Olympic gold medals in any sport. One of the events he won was the 100-meter
Sample versus population in Norway: The Nord-Trøndelag health study surveyed more than 60,000 people in a Norwegian county and reported that gastrointestinal symptoms, depression, and anxiety disorders are strongly related (Haug et al., 2002).a. What is the sample used by these researchers?b. What
Increase in depression globally: According to the World Health Organization (2018a), more than 300 million people suffer from depression globally.a. Do you think the research behind this statistic is based on a sample or a population? Explain.b. Is 300 million a descriptive statistic or an
A study of the effects of skin tone (light, medium, and dark) on the severity of facial wrinkles in middle age might be of interest to dermatologists.a. What would the independent variable be in this study?b. What would the dependent variable be in this study?c. How many levels would the
Suppose a researcher is interested in evaluating how pet ownership and social activity affect loneliness.a. Identify the independent variables and the dependent variable.b. Imagine that pet ownership is assessed as either owning no pets or owning at least one pet, and that social activity is
In the fall of 2008, the 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 money people saved in 2009. That amount could be compared to the amount people saved in more economically
As they leave a popular grocery store, 73 people are stopped and the number of fruit and vegetable items they purchased is counted.a. What is the size of the sample?b. Identify the population.
A researcher studies the average distance that 130 people living in urban areas in India walk each week.a. What is the size of the sample?b. Identify the population.
Over the course of 1 week, a grocery store randomly selected 100 customers to complete a survey about their favorite products. Identify the sample and population for this example.
University bookstore employees asked 225 students to complete a customer satisfaction survey aer these customers bought their books. The bookstore manager wanted to nd ways to improve the customer experience. Identify the sample and population for this example.1
A researcher studies the number of hours 2500 Canadians work out every week. Identify the sample and the population for this example.
What is HARKing and how can preregistration help to eliminate this practice?
What is preregistration and why is it important?
Describe the kinds of unethical practices that researchers might be concerned with.
What do researchers mean by data ethics?
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 statements and supply the correct word.a. A researcher examined the effect of the ordinal
In statistics, it is important to pay close attention to language. The following statements are wrong but can be corrected by substituting one word or phrase. For example, the sentence “Only correlational studies can tell us something about causality” could be corrected by changing
What is the difference between a between-groups research design and a within-groups research design?
What is the difference between experimental research and correlational research?
In your own words, dene the word experiment—rst, as you would use it in everyday conversation and then, as a researcher would use it.
To test a hypothesis, we need operational denitions of the independent and dependent variables. What is an operational denition?
What is the difference between reliability and validity, and how are the two concepts related?
What are confounding variables (or simply confounds), and how are they controlled using random assignment?
What is the relation between an independent variable and a dependent variable?
Distinguish between discrete variables and continuous variables.
Describe two ways that statisticians might use the word scale.
Identify and dene the four types of variables that researchers use to quantify their observations.
What is the difference between a sample and a population?
What is the difference between descriptive statistics and inferential statistics?
Let be iid Bernoulli random variables with unknown parameter p.Construct an approximate Wald test (at level α) for the hypothesis pair vs for p 0 ∈ (0, 1) fixed. Compare this test with the corresponding likelihood ratio test.
Let be an iid sample, where the variance is unknown.Construct an approximate Wald test (at level α) for the hypothesis pair vs , for fixed. Compare this test with the corresponding likelihood ratio test.
(Unpaired Test) Let , be a sample of n + m independent random variables, where and , and is unknown (but the same for the X and the Y ). The goal of this exercise is to determine the LRT for the hypothesis pair vs .Define the likelihood of the parameter?
(Paired Test) A standard problem in the pharmaceutical industry is to determine whether treatment with a new drug will have an effect on a patient. Consider, for instance, the problem of reducing blood pressure, perhaps even by placebo effect. Let X i be the blood pressure of the ith patient before
Let be iid N(μ, 4 2) random variables. We wish to determine whether μ is larger than μ 0 = 10 . To this aim, we carry out a test at level α= 5% contrasting the hypotheses H 0: μ ≤ 10 and H 1: μ > 10.Calculate the power of the test when the true value of μ equals 13 and when it equals
A bio-imaging laboratory has developed a new method to carry out brain scans in less than 20 min. A sample of 12 brain scan durations from the lab is given below:Suppose that the duration time approximately follows an N(μ, 3 2)distribution. Test whether the mean scan time is less than 20 min,
(Intuitive Hypothesis Tests)The goal of this exercise is to motivate hypothesis testing from a more intuitive perspective, via point estimation. Let be iid with density function where is a parameter. We wish to test vs. , where.Find the maximum likelihood estimator .As we have seen in Chapter 3, is
Let and consider the pair and with .Find the most powerful test of H 0 against H 1 at significance level. Consider the behaviour of this level as a function of and n. What is the power of this test? Is it possible to define a Neyman–Pearson optimal test for other values of α?
Given a sample , we wish to test Determine the (approximate) sample size for which both the probability of type I error and the probability of type II error are equal to 0. 01. Use a test function that rejects H 0 when is large. Hint: use the central limit theorem, and recall the last part of
In the context of exercise 41, p. 99, find the smallest value of Q for which the significance level is equal to some α ∈ (0, 1). Evaluate this for α = 0. 05 and n = 10. Find the supremum (over the parameter space) of the probability of type II error for that value of Q.In the context of
(Bonferroni Correction, Multiple Testing)For each j = 1, …, J, let be iid Bernoulli random variables with (unknown) success probability p j∈ (0, 1), and n > 1. Note that the variables are independent for fixed j and varying i, but could dependent for fixed i and varying j (e.g. X ij may be a
Let be an iid sample from the Bernoulli(p) distribution, with p ∈(0, 1) . We will test the null hypothesis against the alternative using the test statistic and the corresponding test function where .Find the probability of committing a type I error.
Let be an iid sample from an N(μ, 1) distribution. We will test H 0: μ = 0 against the alternative H 1: μ ≠ 0 using the test statistic and corresponding test function where Q > 0.Find the probability of committing a type I error.Find the probability of committing a type II error.How do these
We now consider two examples that fall outside of the realm of exponential families.Let , where . Let be the MLE of . Find a sequence of real numbers a n such that converges in distribution to a non-degenerate limit (i.e. not a constant or infinity).Consider , the estimator from exercise 33, p. 74.
Let be a regular parametric model (not necessarily an exponential family) such that does not depend on , and f twice differentiable with respect to . Let. Show that the equality in 3.2 is equivalent to a regularity condition allowing us to interchange integration and differentiation.Reminder: for
Let where both parameters are unknown (n > 1). We can estimate by or by the MLE given by.Which of the two estimators is preferable in terms of mean squared error?
(Cramér–Rao Bound and Exponential Families)Let be a non-degenerate exponential family such that The parameter space is open;T(X) is not a constant function (i.e. ) for all ;The function is a twice differentiable injection with nonvanishing first derivative
(Conditional Likelihood) Let , where . How does the MLE of change if we somehow are told that all X i overshot their mean? (in mathematical terms, conditional on the event ). Note that as with example 3.20, the support of the conditional distribution depends on the true parameter value .
(Minimum Likelihood) Let X be a discrete random variable taking the values
Let , where n > 2, and let be the MLE of on the basis of the sample.
Let x 1, …, x n be independent realisations of a random variable X possessing a continuous density functionf. Show that the histogram converges in probability pointwise to f(y), as , and .Hint: the number of observations in the interval , given by, follows a Binom(n, p n) distribution, where .You
Let , where and consider the probability. We wish to approximate π by where(effectively replacing the true mean in the expression for the probability by the empirical mean). We know that the satisfies the central limit theorem. Show that this also gives a central limit theorem for in the form of
Prove the last lemma.
Let be a sequence of random variables with Show that , but .Suppose, though, that is a constant, and {X n } n ≥ 1 is a sequence such that . Then we have the following result.
Let , where f is of an exponential family form, expressed in the usual parametrisation as . Assuming that is open, show that:If η is k-times continuously differentiable (k ≥ 1), invertible, and, then d is k-times continuously differentiable.
The following table contains the results of rugby matches of the eleventh and twelfth match days (November 2014) of the French rugby first (“Top 14”) and second (“Pro D2”) division. The home team is always mentioned first.
The following data are on the maximal weight (in tons) that could be supported by steel cables produced at a factory:
Let be a sample. What are the median M and quartiles Q 1 and Q 3 when n = 12, 13, 14 or 15? A more tedious generalisation: find the general formulae (for n arbitrary) for the first and third quartile, Q 1 and Q 3. Hint:these formulae are of the form We conclude our brief discussion of numerical
Show that we may also write . Comment on why this formula may be more useful.The sample variance expresses how concentrated or spread out the observations are relative to their sample mean. From a physics point of view, it represents the second moment of inertia around the mean.4 As was the case
Calculate the mean and the median M of the following data set:Exercise 1.16 Show that The function has a unique minimum at .
Prove that the lack of memory property characterises the exponential. More precisely, let X be a random variable such that and Prove that there exists a such that .Hint: Let . Show that the lack of memory property implies that for t, s ≥ 0.Then, define and .Show that for all t > 0 rational.
Prove Lemma 1.32.This last result is particularly important because it allows us to calculate probabilities associated with normal random variables. The problem is that the integral cannot be explicitly solved, and so one would need to tabulate probabilities for all combinations of μ and (an
(Random Number Generation)Let and let F be a distribution function. Prove that the distribution function of the random variable is given precisely by F, where we define (see Definition A.6, p. 161).Observe that with this result, we can generate realisations from any distribution, provided that we
(Log-Normal Distribution) Let , and show that the density of Y = e Xis given by
Show that if and only if .The continuous probability models we have encountered so far have all been restricted either to a bounded interval or to the positive reals. In many phenomena, we expect that the random variable can assume any positive value,
Let X, Y be independent exponential random variables with rates and .Prove that is also exponential with rate .
Let . Then .The exponential distribution is, in fact, the unique distribution on with this property (see Exercise 14, p. 27). Therefore, when choosing the exponential distribution as a model for a random time, we must always ask if it is reasonable to assume that this random time has the lack of
Let and be independent. Show that the conditional distribution of X given is .It would seem that the Poisson distribution came out of nowhere, whereas the other distributions we considered were linked with the Bernoulli distribution. It turns out that there is an important connection between the
Let . Show that
Show that if where , then . Deduce the mean, variance and moment generating function of X.What if we would like to count the number of successes not within a discrete set of trials but within a bounded uncountably infinite set, such as an interval? For example, the total number of calls in a call
Let {Y i } i ≥ 1 be an infinite collection of random variables, where. Let . Then (Figs. 1.1 and 1.2).
Show that if where , then .Example 1.6 Since the binomial is a sum of independent Bernoulli random variables, we can expect that our previous examples can be extended to give us examples of using the binomial distribution (though this is not the case with all of them: we need both independence and
(Project) Obtain quarterly (unadjusted) data for a suitable variable (some suggestions are given below) and examine its seasonal pattern. Write a brief report on your findings. You should:(a) Say what you expect to find, and why.(b) Compare different methods of adjustment.(c) Use your results to
(a) How many seasonal dummy variables would be needed for the regression approach to the data in Problem 11.3?(b) Do you think the approach would bring as reliable results as it did for consumers’ expenditure?
A computer will be needed to solve this and the next problem.(a) Repeat the regression equation from Problem 11.5 but add three seasonal dummy variables (for quarters 2, 3 and 4) to the regressors. (The dummy for quarter 2 takes the value 1 in Q2, 0 in the other quarters. The Q3 dummy takes the
(a) Using the data from Problem 11.3 (2004–14 only), fit a linear regression line to obtain the trend values. By how much, on average, does car production increase per year?(b) Calculate the seasonal factors (multiplicative model). How do they compare to the values in Problem 11.3?(c) Predict car
(a) Using the data of Problem 11.1, fit a regression line through the data, using t and t2 as explanatory variables (t is a time trend 1–36). Use only the observations from 2000 to 2014. Calculate the trend values using the regression.(b) Calculate the seasonal factors (multiplicative model)
Repeat Problem 11.3 using the additive model and compare results.
The following data relate to car production in the United Kingdom (not seasonally adjusted).(a) Graph the data for 2004–14 by overlapping the three years (as was done in Figure 11.2) and comment upon any seasonal pattern.(b) Use a 12-month moving average to find the trend values for 2004–14.(c)
Repeat the exercise using the additive model. (In Problem 11.1(c), subtract the moving average figures from the original series. In (e), subtract the seasonal factors from the original data to get the adjusted series.) Is there a big difference between this and the multiplicative model?
The following table contains data for consumers’ non-durables expenditure in the United Kingdom, in constant 2003 prices.(a) Graph the series and comment upon any apparent seasonal pattern. Why might it occur?(b) Use the method of centred moving averages to find the trend values for 2000–14.(c)
(Project) The World Development Report contains data on the income distributions of many countries around the world (by quintile). Use these data to compare income distributions across countries, focusing particularly on the differences between poor countries, middle-income and rich countries. Can

Showing 800 - 900 of 5435

First
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Last

Statistics For Economics Accounting And Business Studies 7th Edition Michael Barrow - Solutions

Step by Step Answers