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statistical techniques in business

Questions and Answers of Statistical Techniques in Business

A report by the Gallup organization in February 2015 estimated that 9% of Republicans approved of President Barack Obama’s performance, whereas 79% of Democrats approved.Would you characterize the
Table 8.23, from the 2014 General Social Survey, cross-classifies happiness and marital status.(a) Software reports that X2 = 135.3.Interpret.(b) The table also shows, in parentheses, the
For a 2×4 cross-classification of gender and religiosity(very, moderately, slightly, not at all) for recent GSS data, the standardized residual was 3.2 for females who are very religious, −3.2 for
Table 8.22 shows SPSS analyses with the 2014 General Social Survey, for variables party ID and race.(a) Report the expected frequency for the first cell, and show how SPSS obtained it.(b) Test the
The sample in Table 8.16 is 382 black Americans.Table 8.21 shows cell counts and standardized residuals for income and happiness for white subjects in the 2014 General Social Survey.(a) Interpret the
In the GSS, subjects who were married were asked the happiness of their marriage, the variable coded as HAPMAR.(a) Go to sda.berkeley.edu/GSS/ and construct a contingency table for 2014 relating
Are people happier who believe in life after death?Go to the GSS website sda.berkeley.edu/GSS and download the contingency table for the 2014 survey relating happiness and whether you believe in life
Table 8.20 is based on results described in a study5 that examined the effects of alcohol consumption and drug use on sexual behavior, for undergraduate students at a university in the southeastern
In 2010, the GSS asked about willingness to accept cuts in the standard of living to help the environment, with categories (very willing, fairly willing, neither willing nor unwilling, not very
A sociologist uses a 2 × 4 contingency table to compare four groups on a binary response variable. For group i, let πi denote the population proportion of response in the first outcome category, i
How large a X2 value provides a P-value of 0.05 for testing independence for the following table dimensions?(a) 2 × 2 (b) 3 × 3 (c) 2 × 5 (d) 5 × 5(e) 3 × 9
Data posted at the FBI website (www.fbi.gov) indicated that of all blacks slain in 2013, 92% were slain by blacks, and of all whites slain in 2013, 93% were slain by whites. Let y denote race of
Based on current estimates of how well mammograms detect breast cancer, Table 8.19 shows what to expect for 100,000 adult women over the age of 40 in terms of whether a woman has breast cancer and
TheWorld Values Survey4 asked, “How often do you pray?” The response never was given by 16.5% of the 2232 respondents in the United States, by 48.4% of the 1189 respondents in Spain, and by 56.8%
A March 2015 survey by the Pew Research Center(www.pewresearch.org) compared various groups of Americans in terms of their support for legalizing marijuana.In considering age groups, it estimated
Whether a woman becomes pregnant in the next year is a categorical variable with categories (yes, no), and whether she and her partner use contraceptives is another categorical variable with
GSS surveys routinely show that in the United States, about 40% of males and 40% of females believe that a woman should be able to get an abortion if she wants it for any reason.(a) Construct a
For (a)–(c), is it a null hypothesis, or an alternative hypothesis?(a) In Canada, the proportion of adults who favor legalized gambling equals 0.50.(b) The proportion of all Canadian college
You want to know whether adults in your country think the ideal number of children is equal to 2, or higher or lower than that.(a) Define notation and state the null and alternative hypotheses for
For a test of H0: μ = 0 against Ha: μ = 0 with n = 1000, the t test statistic equals 1.04.(a) Find the P-value, and interpret it.(b) Suppose t = −2.50 rather than
Find the P-value.Does this provide stronger, or weaker, evidence against the null hypothesis? Explain.(c) When t = 1.04, find the P-value for (i) Ha: μ > 0,(ii) Ha:μ < 0.
The P-value for a test about a mean with n = 25 is P = 0.05.(a) Find the t test statistic value that has this P-value for (i) Ha: μ = 0, (ii) Ha:μ > 0, (iii) Ha:μ < 0.(b) Does this P-value
Find and interpret the P-value for testingH0: μ = 100 against H0: μ = 100 if a sample has(a) n = 400, ¯y = 103, and s = 40.(b) n = 1600, ¯y = 103, and s = 40. Comment on the effect of n on the
Example 6.4 (page 148) described a study about therapies for teenage girls suffering from anorexia. For the 17 girls who received the family therapy, the changes in weight were 11, 11, 6, 9, 14,
According to a union agreement, the mean income for all senior-level workers in a large service company equals $500 per week. A representative of a women’s group decides to analyze whether the mean
By law, an industrial plant can discharge no more than 500 gallons of waste water per hour, on the average, into a neighboring lake. Based on other infractions they have noticed, an environmental
In response to the statement “A preschool child is likely to suffer if his or her mother works,” the response categories (Strongly agree, Agree, Disagree, Strongly disagree)had counts (91, 385,
In Example 6.2 on political ideology (page 145), suppose we use the scores (−3, −2, −1, 0, 1, 2, 3) instead of(1, 2, 3, 4, 5, 6, 7). We then test H0: μ = 0. Explain the effect of the change in
Results of 99% confidence intervals for means are consistent with results of two-sided tests with which α-level? Explain the connection.
For a test of H0: π = 0.50, the z test statistic equals 1.04.(a) Find the P-value for Ha:π > 0.50.(b) Find the P-value for Ha: π = 0.50.(c) Find the P-value for Ha:π < 0.50.(d) Do any of the
For a test of H0: π = 0.50, the sample proportion is 0.35 with n = 100.(a) Show that the test statistic is z = −3.0.(b) Find and interpret the P-value for Ha:π < 0.50.(c) For a significance level
Same-sex marriage was legalized across Canada by the Civil Marriage Act enacted in 2005. Is this supported by a majority, or a minority, of the Canadian population?In an Ipsos Global poll conducted
When the 2010 General Social Survey asked,“Would you be willing to pay much higher taxes in order to protect the environment?” 459 people answered yes and 626 answered no. Software shows the
TheWorld Values Survey12 asked, “Indicate the importance in your life of religion.” Of the people sampled in the Netherlands, Stata reports the following output for the proportion who answered,
In the scientific test of astrology discussed in Example 6.9 (page 163), the astrologers were correct with 40 of their 116 predictions. Test H0: π = 1/3 against Ha: π >1/3. Find the P-value, make a
The previous exercise analyzed whether astrologers could predict the correct personality chart for a given horoscope better than by random guessing. In the words of that study, what would be a (a)
A mayoral election in Madison, Wisconsin, has two candidates. Exactly half the residents currently prefer each candidate.(a) For a random sample of 400 voters, 230 voted for a particular candidate.
The authorship of an old document is in doubt.A historian hypothesizes that the author was a journalist named Jacalyn Levine. Upon a thorough investigation of Levine’s known works, it is observed
A multiple-choice test question has four possible responses. The question is difficult, with none of the four responses being obviously wrong, yet with only one correct answer. It first occurs on an
Example 6.4 (page 148) tested a therapy for anorexia, using H0: μ = 0 and Ha:μ > 0 about the population mean weight change.(a) In the words of that example, what is a (i) Type I error? (ii) Type II
Jones and Smith separately conduct studies to test H0: μ = 500 against H0: μ = 500, each with n = 1000.Jones gets ¯y = 519.5, with se = 10.0.Smith gets ¯y = 519.7, with se = 10.0.(a) Show that t
Jones and Smith separately conduct studies to test H0: π = 0.50 against H0: π = 0.50, each with n =400. Jones gets πˆ = 220/400 = 0.550.Smith gets πˆ =219/400 = 0.5475.(a) Show that z = 2.00
A study considers whether the mean score μ on a college entrance exam for students in 2016 is any different from the mean of 500 for students in 1966. Test H0:μ = 500 against Ha: μ = 500 if for a
Areport by the Collaborative onAcademic Careers in Higher Education indicated that there is a notable gap between female and male academics in their confidence that tenure rules are clear, with men
Refer to Example 6.8 on “medical discoveries”(page 161). Using a tree diagram, approximate P(Type I error) under the assumption that a true effect exists 20%of the time and that P(Type II error)
A decision is planned in a test of H0: μ = 0 against Ha: μ > 0, using α = 0.05.If μ = 5, P(Type II error) =0.17.(a) Explain the meaning of this last sentence.(b) If the test used α = 0.01, would
Let π denote the proportion of schizophrenics who respond positively to treatment.Atest is conducted ofH0:π = 0.50 against Ha:π > 0.50, for a sample of size 25, usingα = 0.05.(a) Find the region
A follow-up to the anorexia study of Example 6.4 plans a test of H0: μ = 0 against Ha: μ > 0, for the mean weight change μ for a new therapy, predicting that μ = 10.The test uses α = 0.05.For n
Refer to the previous exercise.(a) Find P(Type II error) if μ = 5. How does P(Type II error) depend on the value of μ?(b) Find P(Type II error) if μ = 10 and α = 0.01.How does P(Type II error)
A jury list contains the names of all individuals who may be called for jury duty. The proportion of women on the list is 0.53.A jury of size 12 is selected at random from the list. None selected are
A person claiming to possess extrasensory perception(ESP) says she can guess more often than not the outcome of a flip of a balanced coin in another room, not visible to her.(a) Introduce appropriate
In aCNNexit poll of 1336 voters in the 2006 Senatorial election in NewYork State, let x =number in exit poll who voted for the Democratic candidate, Hillary Clinton.(a) Explain why this scenario
In a given year in the United States, the probability of death in a motor vehicle accident equals 0.0001 for females and 0.0002 for males (Statistical Abstract of the United States).(a) In a city
You can use the Errors and Power applet at www.artofstat.com/webapps.html to investigate the performance of significance tests, to illustrate their long-run behavior when used for many samples. For
Refer to the Students data file (Exercise 1.11 on page 9).(a) Test whether the population mean political ideology differs from 4.0.Report the P-value, and interpret.(b) Test whether the proportion
Refer to the data file your class created in Exercise 1.12 (page 10). For variables chosen by your instructor, state a research question and conduct inferential statistical analyses. Also, use
A study considered the effects of a special class designed to improve children’s verbal skills. Each child took a verbal skills test before and after attending the class for three weeks. Let y =
The 49 students in a class at the University of Florida made blinded evaluations of pairs of cola drinks. For the 49 comparisons of Coke and Pepsi, Coke was preferred 29 times. In the population that
The U.S. Justice Department and other groups have studied possible abuse by police officers in their treatment of minorities. One study, conducted by the American Civil Liberties Union, analyzed
An experiment with 26 students in an Israeli classroom consisted of giving everyone a lottery ticket and then later asking if they would be willing to exchange their ticket for another one, plus a
Ideally, results of a statistical analysis should not depend greatly on a single observation. To check this, it’s a good idea to conduct a sensitivity study: Redo the analysis after deleting an
In making a decision in a test, a researcher worries about the possibility of rejecting H0 when it is actually true. Explain how to control the probability of this type of error.
Consider the analogy between making a decision in a test and making a decision about the innocence or guilt of a defendant in a criminal trial.(a) Explain what Type I and Type II errors are in the
Medical tests for diagnosing conditions such as breast cancer are fallible, just like decisions in significance tests. Identify (H0 true, H0 false) with disease (absent, present), and (Reject H0, Do
An article in a sociology journal that deals with changes in religious beliefs over time states, “For these subjects, the difference in their mean responses on the scale of religiosity between age
An article in a political science journal states that“no significant difference was found between men and women in their voting rates (P = 0.63).” Can we conclude that the population voting rates
You conduct a significance test using software. The output reports a P-value of 0.4173545. In summarizing your analyses in a research article, explain why it makes more sense to report P = 0.42
A research study conducts 60 significance tests. Of these, three are significant at the 0.05 level. The authors write a report stressing only the three “significant”results, not mentioning the
Some journals have a policy of publishing research results only if they achieve statistical significance at the 0.05 α-level.(a) Explain the dangers of this.(b) When medical stories in the mass
We analyze whether the true mean discharge of wastewater per hour from an industrial plant exceeds the company claim of 1000 gallons. For the decision in the one-sided test using α = 0.05,(a) If the
The P-value for testing H0: μ = 100 against Ha:μ = 100 is P = 0.001.This indicates that(a) There is strong evidence that μ = 100.(b) There is strong evidence that μ = 100.(c) There is strong
In the previous exercise, suppose the test statistic z = 3.29.(a) There is strong evidence that μ = 100.(b) There is strong evidence thatμ > 100.(c) There is strong evidence thatμ < 100.
A 95% confidence interval for μ is (96, 110).Which two statements about significance tests for the same data are correct?(a) In testing H0: μ = 100 against Ha: μ = 100, P > 0.05.(b) In testing
Let β denote P(Type II error). For an α = 0.05-level test of H0: μ = 0 against Ha: μ > 0 with n = 30 observations,β = 0.36 at μ = 4. Then,(a) At μ = 5,β > 0.36.(b) If α = 0.01, then at μ =
Answer true or false for each of the following, and explain your answer:(a) P(Type II error) = 1 − P(Type I error).(b) If we reject H0 using α = 0.01, then we also reject it using α = 0.05.(c)
Explain the difference between one-sided and twosided alternative hypotheses, and explain how this affects calculation of the P-value.
Your friend plans to survey students in your college to study whether a majority feel that the legal age for drinking alcohol should be reduced. He has never studied statistics. How would you explain
A random sample of size 40 has ¯y = 120. The Pvalue for testing H0: μ = 100 against Ha: μ = 100 is P = 0.057.Explain what is incorrect about each of the following interpretations of this P-value,
Refer to the previous exercise and the P-value of 0.057.(a) Explain why the P-value is the smallest α-level at which H0 can be rejected; that is, P equals the smallest level at which the data are
Aresearcher conducts a significance test every time she analyzes a new data set. Over time, she conducts 100 tests.(a) Suppose H0 is true in every case. What is the distribution of the number of
Each year in Liverpool, New York, a public librarian estimates the mean number of times the books in that library have been checked out in the previous year. To do this, the librarian randomly
Refer to Example 5.8 on 0 vegetarians in a sample of n = 20 and Exercises 5.77 and 5.77.(a) At the Inference for a Proportion applet at www.artofstat.com/webapps.html, enter 0 successes for n = 20.
You test H0: π = 0.50 against Ha: π > 0.50, usingα = 0.05.In fact, Ha is true. Explain why P(Type II error) increases toward 0.95 as π moves down toward 0.50.(Assume n and α stay fixed. You may
Refer to the ESP experiment in Exercise 6.33, with n = 5.(a) For what value(s) of x = number of correct guesses can you reject H0: π = 0.50 in favor of Ha:π > 0.50, usingα = 0.05?(b) For what
12.1. Vertex operators In order to prove that the ground states | α of the free bosonic theory are obtained by applying the vertex operators Vα(z,¯0) to the conformal vacuum | 0 it is necessary
12.2. Modular transformations of the θi(τ ) functions.Let us denote by θi(z,τ) the theta functions of Jacobi, with θ1(τ ) = 0, while the others have the infinite series and product
12.3. Dedekind function The Dedekind function is defined by the infinite product (q = e2iπτ )η(τ ) = q1/24∞n=1(1−qn).a. Use the definition of the θi(τ ) functions in terms of the infinite
12.4. Bosonic partition function at the self-dual point Consider the expression (12.2.56) of the partition function of a bosonic field with a compactification radius R equal to the self-dual value R
12.5. Jacobi identity The aim of this exercise is to prove, by physical arguments, the Jacobi identity∞n=1(1−qn)(1+qn−1/2w)(1+qn−1/2w−1) =∞n=−∞qn2/2wn that holds for |q| < 1 and w
12.6. Quantum Pythagorean theorem A regularization of the normal order : A(x)B(x) : of two operators can be obtained by the limit limη→0 : A(x−η/2)B(x+η/2) : and an average on all directions
12.7. Equivalence of the Sine–Gordon and Thirring models Consider the Sine–Gordon model of a scalar bosonic field ϕ, whose Lagrangian is L = 1 2(∂ϕ)2 + m2β2 (cosβϕ −1).Use the
13.1. Spontaneous supersymmetry breaking Let Q be the generator of a N = 1 supersymmetric theory and Q† its adjoint operator.With a proper normalization we have{Q,Q†} = H, where H is the
13.2. Central charge of the parafermions On a physical basis argue why in the limitN→∞the central charge of the parafermionic systems is equal to c = 2.
13.3. Polyakov–Wiegman identity Consider the action of the sigma model with a Wess-Zumino topological term S(g) = k 16πd2xTr(∂μg−1∂μg)+k.Prove the identity S(gh−1) = S(g)+S(h)+ k
13.4. Correlation functions of the currents For the conformal models with a Kac–Moody algebra, compute the-point correlation functions of the analytic currents Ja(z1)Jb(z2)Jc(z3)Jd(z4).
13.5. Bosonization of the SU(2)1 theory Verify that the central charge of the theory SU(2)1 is c = 1. Compute the spectrum of the conformal weights of this theory and determine a representation of
14.1. Correlator of the Ising model Consider the following correlator of the two-dimensional Ising model H(η, ¯ η) = σ(∞)(1,1)(η, ¯ η)σ(0,0).Use the modified Coulomb gas to show that it
14.2. Structure constants Use the modified Coulomb gas to compute the correlation functions of the TIM.Determine the values of the structure constants given in the text.14.3. Vacua of the
16.1. Backlund transformationsa. Write down the Backlund transformations for the Sine–Gordon model.b. Taking as initial solution of the equation of motion φ = 0, determine the new solution ˆ
16.2. Scattering processes of the solitons Analyse the solution (16.3.15) with topological charge T = 2 of the Sine–Gordon model in the limits t→±∞. Determine the time delay ss. Based on the

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