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Statistical Methods For The Social Sciences 5th Global Edition Alan Agresti - Solutions

Table 7.17 summarizes the number of hours spent in laboratory per week by researchers, based on a recent study.(a) Estimate the difference between population means for junior and senior fellows.(b) Show that the estimated standard error of the sample difference is 0.58.Interpret.(c) Show that a 99%
A GSS reported that the 486 females had a mean of 8.3 close friends (s = 15.6) and the 354 males had a mean of 8.9 close friends (s = 15.5).(a) A 95% confidence interval for the difference between the population means for males and for females is (−1.5, 2.7). Interpret.(b) For each sex, does it
Table 7.16 shows results from the 2014 General Social Survey on belief in an afterlife, classified by sex. Conduct all steps of a significance test, using α = 0.05, to compare the population proportions of females and males who would respond yes to belief in an afterlife. If you have made an error
A study of compulsive buying behavior (uncontrolled urges to buy) conducted a national telephone survey in 2004 of adults ages 18 and over.13 Of 800 men, 44 were judged to be compulsive buyers according to the Compulsive Buying Scale. Of 1501 women, 90 were judged to be compulsive buyers. Conduct
In a survey conducted by the education department, college teachers were asked if they frequently used interactive teaching learning methods. Table 7.15 shows software output. Treating these observations as a random sample from the population of interest,(a) State a research question that could be
Refer to the previous exercise. In 2014, of 745 male respondents, 247 (33.2%) agreed. Of 910 female respondents, 268 (29.5%) agreed.(a) Set up notation and specify hypotheses for the hypothesis of no difference between the population proportions of males and of females who would agree.(b) Estimate
Table 7.14 summarizes responses from General Social Surveys in 1977 and in 2014 to the statement “It is much better for everyone involved if the man is the achiever outside the home and the woman takes care of the home and family.” Let π1 denote the population proportion who agreed with this
In Great Britain, the Time Use Survey(www.statistics.gov.uk) studied how a random sample of Brits spend their time on a typical day. Of those working full time, 55% of 1219 men and 74% of 733 women reported spending some time on cooking and washing up during a typical day. Find and interpret a
The study mentioned in the previous exercise estimated in 2010 that 3% had done better in interschool competitions because of reading such books; this was 4.5% at the latest survey.(a) Specify assumptions, notation, and hypotheses for a two-sided test comparing the corresponding population
A study group at a high school has interviewed random samples of students at higher grades several times since 2010. Most recently, of the students who reported reading Encyclopedia Britannica, the percentage who reported that reading “to portray their image as studious”is an important reason
For a random sample of university teachers, 50%were positive about the vice chancellor’s performance. A similar poll two months later indicated an approval rate of 47%. A 99% confidence interval for the change in the population proportions is (−0.09, 0.03). Explain why(a) there may have been no
The Global Charitable Trust asked, “How often do you donate?” The response sometimes was given by 22.1% of the 1532 respondents in Country A and by 46.7% of the 1098 respondents in Country B.(a) Assuming random sampling, the 95% confidence interval for the difference between corresponding
According to a university database, the annual probability that a student between the ages of 20 and 24 fails to go abroad for higher studies is 0.00237 for males and 0.00069 for females.(a) Compare these rates using the difference of proportions.(b) Compare these rates using the ratio of
In 2016, the EducationalResearchWing reported that the school dropout rate in a country was 375 per 10,000 male students (composed of 8% of urban male students and 12% of rural male students), and 425 per 10,000 female students.(a) Find the ratio of proportions of dropouts, for females relative to
In 2015, a country’s planning commission estimated its median household consumption expenditure in domestic currency to be 265,000 in urban and 51,000 in rural sectors.(a) Identify the response variable and the explanatory variable.(b) Compare the households using a (i) difference,(ii) ratio.
The Regional Center for Health Survey recently estimated that the mean weight for adult Indian women was 52 kg in 1968 and 65 kg in 2012.(a) Suppose these estimates had a standard error of 1.2 kg each year. Estimate the increase in mean weight in the population from 1968 to 2012, and find and
When a recent Eurobarometer survey asked subjects in each European Union country whether they would be willing to pay more for energy produced from renewable sources than for energy produced from other sources, the proportion answering yes varied from a high of 0.52 in Denmark (n = 1008) to a low
An annual survey on consumer expenditure for a country estimated 56% of its citizens to own large cars in 2017 as compared to 29% in 2012.(a) Estimate the difference between the proportions of large car owners over the periods.(b) If standard error is 0.040 for each proportion, find the standard
An annual survey of public opinion considers the public views about adequacy of policies taken to protect global environment, with a random sample of about 5000 adults from each of 20 developing nations each year. In 2000, 15% of them expressed positive views about adequacy of the measures taken at
The biannual ABDC survey of school students indicated that 78% of tenth graders in 2016 considered having a car to be essential or very important, compared to 45%when the survey was first conducted in 1968. Are the sample percentages of 45% in 1968 and 78% in 2016 based on independent samples, or
You evaluate 16 schools in your city over the past four years according to the change from the previous year in the mean student score on a standardized achievement test. Of the schools, school number 3 performed above the median in all four years. Explain what is misleading if you use this record
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 value(s) of x can you reject H0 using α =0.01? (Note: For small samples, it may not be possible to
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 want to look at the applet introduced in Exercise 6.36.)
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.pearsonglobaleditions.com/Agresti, enter 0 successes for n = 20. Explain why the reported standard error values differ when you click on Confidence Interval
11.65.* Let ¯b∗i denote the estimated standardized regression coefficient when xi is treated as the response variable and y as an explanatory variable, controlling for the same set of other variables. Then, ¯b∗i need not equal b∗i. The squared partial correlation between y and xi, which is
Each year in an archive at New Delhi, the director estimates the mean number of times the archived documents have been checked out in the previous year. To do this, the director randomly samples computer records for 500 books and forms a 95% confidence interval for the mean. This has been done for
A surveyor conducts a significance test every time he analyzes a new survey data. Over time, he conducts 200 tests.(a) Suppose H0 is true in every case. What is the distribution of the number of times she rejects H0 at the 0.01 level?(b) Suppose she rejects H0 in seven of the tests. Is it plausible
Refer to the previous exercise and the P-value of 0.069.(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 significant.(b) Refer to the correspondence between results of confidence intervals and two-sided
A random sample of size 50 has ¯y = 130. The P-value for testing H0: μ = 120 against Ha: μ = 120 is P = 0.069.Explain what is incorrect about each of the following interpretations of this P-value, and provide a proper interpretation.(a) The probability that the null hypothesis is correct equals
A researcher plans to survey people in your locality to study whether a majority feel that the cap on foreign direct investment should be reduced. The researcher has never studied statistics. How would you explain to him the concepts of (a) null and alternative hypotheses,(b) P-value, (c) α-level,
Explain the difference between one-sided and twosided alternative hypotheses, and explain how this affects calculation of the P-value.
Answer true or false for each of the following, and explain your answer:(a) P (Type II error) always increases with P (Type I error).(b) If we accept HA using α = 0.01, then we also accept it using α = 0.05.(c) The P-value is the probability that HA is false. (Hint:Do we find probabilities about
Let β denote P (Type II error). For an α = 0.01-level test of H0: μ = 0 against Ha: μ > 0 with n = 50 observations, β = 0.57 at μ = 6. Then,(a) At μ = 6,β > 0.57.(b) If n = 80, then at μ = 6,β > 0.57.(c) If α = 0.01, then at μ = 6,β > 0.57(d) The power of the test is 0.43 at μ = 6.(e)
A 99% confidence interval for μ is (99, 116).Which two statements about significance tests for the same data are correct?(a) In testing H0: μ = 110 against Ha: μ = 110, P < 0.01.(b) In testing H0: μ = 110 against Ha: μ = 110, P > 0.01.(c) In testing H0: μ = μ0 against Ha: μ = μ0, P >
In the previous exercise, suppose the test statistic z = −5.48.(a) There is strong evidence thatμ > 50.(b) There is strong evidence thatμ < 50.(c) There is strong evidence that μ = 50.
The P-value for testing H0: μ = 50 against Ha:μ = 50 is P = 0.003.This implies that(a) There is strong evidence that μ = 50.(b) There is strong evidence that μ = 50.(c) There is strong evidence thatμ > 50.(d) There is strong evidence thatμ < 50.(e) If μ were equal to 50, it would be
We analyze whether the true mean daily discharge of waste by a chemical plant exceeds its claim of 1500 units. For the decision in the one-sided test using α = 0.01,(a) If the plant is not exceeding the limit, but actuallyμ = 1500, there is only a 1% chance that we will conclude that they are not
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 media report supposed large dangers or benefits of certain agents (e.g., coffee drinking, fiber in
A social study conducts 1000 significance tests. Of these, 50 are significant at the 0.05 level. The researchers write a report stressing only the 50 “significant” results, not mentioning the other 950 tests that were “not significant.”Explain what is misleading about their report.
Harry conducted a significance test using Stata. The output reports a P-value of 0.3598621. In summarizing analyses in an article, explain why it would be sensible for Harry to report P = 0.36 rather than P = 0.3598621.
A popular psychology analysis journal reports that“no significant difference was found between Emotional Intelligence Quotient for the academicians and service holders (P = 0.85).” Hence, the population emotional intelligence quotients would be identical for academicians and service
An article in a management journal that deals with changes in social skill over time states, “For these subjects, the difference in their mean performances on a scale of skill between age 25 and the current survey was significant(P < 0.01).”(a) Explain what it means for the result to be
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 not reject H0) with diagnostic test (positive, negative), where a positive diagnosis means that the
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 trial.(b) Explain intuitively why decreasing P(Type I error) increases P(Type II error).(c) Defendants
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.
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 outlier from the data set or changing its value to a more typical value, and check whether results
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 small monetary incentive.Only 7 students agreed to the exchange. In a separate experiment, 31 students
Researchers have studied possible abuse by security officers in treating owner-drivers of small cars at crossroads.An NGO studied whether owner-drivers of small cars were more likely than others in the population to be targeted by officers for traffic stops. They considered 360 car stops due to
Sixty students in a class at the University of Florida made blinded evaluations of pairs of dark chocolates. For 60 comparisons of two chocolates, the first one was preferred 41 times. In the population that this sample represents, is there a strong evidence that a majority prefers one of the
11.66.* Chapters 12 and 13 show how to incorporate categorical explanatory variables in regression models. This exercise provides a preview. Table 11.25 shows some output for a model for the Houses2 data set at the text website, with y = selling price of home, x1 = size of home, and x2 = whether
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 = second exam score − first exam score. The scores on y for a random sample of four children having
Refer to the data file your class created in Exercise 1.12 (page 22). For variables chosen by your instructor, state a research question and conduct inferential statistical analyses. Also, use graphical and numerical methods presented earlier in this text to describe the data and, if necessary, to
Refer to the Students data file (Exercise 1.11 on page 21).(a) Test whether the population mean political ideology differs from 4.0.Report the P-value, and interpret.(b) Test whether the proportion favoring legalized abortion equals, or differs, from 0.50.Report the P-value, and interpret.
You can use the Errors and Power applet at www.pearsonglobaleditions.com/Agresti to investigate the performance of significance tests, to illustrate their long-run behavior when used for many samples. For significance tests, set the null hypothesis as H0: π = 0.50 for a one-sided test with Ha:π >
In a given year in a developing country, the probability of death in any earthquake equals 0.0004 for highlanders and 0.0003 for plain land dwellers (Statistical Abstract of the Developing Countries).(a) In a town having 2 million highland dwellers, find the mean and standard deviation of x =
In a newspaper exit poll of 1500 voters in the 2015 general election in an emerging nation, let x = number of voters in the exit poll who voted for a candidate, Mr. X.(a) Explain why this scenario would seem to satisfy the three conditions needed to use the binomial distribution.(b) If the
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 notation, and state hypotheses for testing her claim.(b) Of five coin flips, she guesses the
An employee list contains the names of all employees who may be deputed with additional charges. The proportion of women on the list is 0.56.A group of size 15 is selected at random from the list. None selected are women.(a) Find the probability of selecting 0 women.(b) Test the hypothesis that the
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) depend on α?(c) How does P(Type II error) depend on n?
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 = 30, suppose the standard deviation is 18. Find P(Type II error) if μ = 10 by showing(a) a test
Let π denote the proportion of people under stress who respond positively to treatment. A test is conducted of H0: π = 0.60 against Ha: π > 0.60, for n = 30, usingα = 0.05.(a) Find the region of sample proportion values for which H0 is rejected.(b) Suppose that π = 0.70.Find 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 P(Type II error) be less than, equal to, or greater than 0.17? Explain.(c) If μ = 10, would P(Type
Refer to Example 6.8 on “medical discoveries”(page 173). 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) = 0.30.
An academic survey on employees at their job market entry level reported the presence of a notable gap between graduate and postgraduate employees in their confidence that tenure rules are clear, with postgraduates feeling more confident. The 4500 staff members in the survey were asked to evaluate
A study considers whether the mean score μ on an MBA entrance exam for students in 2017 was any different from the mean of 400 for students in 1966. Test H0:μ = 400 against Ha: μ = 400 if for a nationwide random sample of 9,000 students who took the exam in 2017,¯y = 397 and s = 90. Show that
Nora and Oliva separately conduct studies to test H0: π = 0.45 against H0: π = 0.45, each with n = 485.Nora gets πˆ = 240/485 = 0.494845 Oliva gets πˆ =239/485 = 0.492784.(a) Show that z = 1.99 and P-value = 0.046 for Nora.Show that z = 1.89 and P-value = 0.058 for Oliva.(b) Using α = 0.05,
Nora and Ayush separately conduct studies to test H0: μ = 400 against HA: μ = 400, each with n = 1200.Nora gets ¯y = 423.35 with se = 12.0.Ayush gets¯y = 434.2, with se = 17.0(a) Show that t = 1.95 and P-value = 0.051 for Nora.Show that t = 2.01 and P-value = 0.044 for Ayush.(b) Using α =
Example 6.4 (page 160) 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 error?(b) The P-value was 0.018.If the decision for α = 0.05 were in error, what type of error is
Amultiple-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 exam taken by 500 students.Test whether more people answer the question correctly than would be
The authorship of an old document is in doubt. An academician hypothesizes that the author was a sociologist named Olivia Munn. Upon a thorough investigation of Munn’s known works, it is observed that one unusual feature of her writing was that she consistently began 5%of her sentences with the
A secretary election in a labor union has two candidates.Exactly half the members currently prefer each candidate.(a) For a random sample of 500 voters, 290 voted for a particular candidate. Are you willing to predict the winner?Why?(b) For a random sample of 50 voters, 29 voted for a particular
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) Type I error? (b) Type II error?
In the scientific test of astrology discussed in Example 6.9 (page 175), 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 decision using α = 0.05, and interpret.
The International EQ Survey asked, “Indicate the importance of honesty in your life.” Of the people sampled in a country, Stata reports the following output for the proportion who answered “very important” or “rather important” (instead of “not very important” or “not at all
When the 2015 Heritage Conservation Survey asked, “Would you be willing to pay higher taxes in order to protect the heritage buildings?” 429 people answered yes and 726 answered no. Software shows the following results to analyze whether a majority or a minority of people would answer
Illegal trafficking of some items in a country was banned by its government in 2007. Is this supported by a majority, or a minority, of the population of the country?In a global poll conducted by an international agency for a reputed newspaper in January 2010 involving 900 residents of the country
For a test of H0: π = 0.60, the sample proportion is 0.45 with n = 125.(a) Show that the test statistic is z = −3.423.(b) Find and interpret the P-value for Ha:π < 0.60.(c) For a significance level of α = 0.01, what decision do you make?(d) If the decision in (c) was an error, what type of
For a test of H0: π = 0.45, the z test statistic equals 0.80.(a) Find the P-value for Ha:π > 0.45.(b) Find the P-value for Ha: π = 0.45.(c) Find the P-value for Ha:π < 0.45.(d) Do any of the P-values in (a), (b), or (c) give strong evidence against H0? Explain.
Results of 95% confidence intervals for means are consistent with results of two-sided tests with whichα-level? Explain the connection.
In Example 6.2 on political ideology (page 157), 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 scores on (a) the sample mean and standard deviation, (b) the test statistic, (c) the P-value and
In response to the statement “An effective leader must be able to feel the emotions of his group-members,”the response categories (Strongly agree, Agree, Disagree, Strongly disagree) had counts (103, 375, 425, 97) for responses in an Emotional Quotient Survey. To treat this ordinal variable as
By law, a chemical plant can discharge no more than 400 units of chemical waste per hour, on an average, into a neighboring river. Based on other infractions they have noticed, an environmental action group believes this limit is being exceeded. Monitoring the plant is expensive, and a random
According to a union agreement, the mean income for all managers in a large manufacturing company equals$2000 per month. A representative of a graduate group decides to analyze whether the mean income μ for graduate managers matches this norm. For a random sample of 10 graduate employees, ¯y =
Example 6.4 (page 160) 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, −3, 0, 7, 22, −5, −4, 13, 13, 9, 4, 6, 11.Some Stata output (edited) for the data
Find and interpret the P-value for testing H0: μ = 50 against H0: μ = 50 if a sample has(a) n = 200, ¯y = 53, and s = 20.(b) n = 800, ¯y = 53, and s = 20. Comment on the effect of n on the results of a significance test.
The P-value for a test about a mean with n = 31 is P = 0.01.(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 provide stronger, or weaker, evidence against the null hypothesis than P = 0.001?Explain.
For a test of H0: μ = 0 against Ha: μ = 0 with n = 1500, the t test statistic equals 0.92.(a) Find the P-value, and interpret it.(b) Suppose t = −3.60 rather than 0.92.Find the P-value.Does this provide stronger, or weaker, evidence against the null hypothesis? Explain.(c) When t = 0.92, find
You want to know whether employees in a company consider the ideal average working hours to be 10, or higher or lower than that.(a) Define notation and state the null and alternative hypotheses for studying this.(b) For responses in a recent survey to the question“What do you think are the ideal
11.67.* Refer to the previous exercise. When we add an interaction term, we get ˆy = −16.6 + 66.6x1 − 31.8x2 +29.4(x1x2).(a) Interpret the fit by reporting the prediction equation between selling price and size of house separately for new homes (x2 = 1) and for old homes (x2 = 0).
For (a)–(c), is it a null hypothesis, or an alternative hypothesis?(a) In India, the proportion of teenagers who watch horror movies equals 0.45.(b) The proportion of all Indian school students with access to the Internet is now more than 0.30 (the value it was 5 years ago).(c) The mean IQ of
This exercise presents a confidence interval for the population median that requires no assumption about the population distribution other than it is essentially continuous.(a) Explain why for a random sample of size n the sample proportion πˆ falling below themedian has expected value 0.50 and
Refer to the previous exercise. At the Inference for a Proportion applet at www.pearsonglobal editions.com/Agresti, enter 0 successes for n = 20.Click on Confidence Interval for type of inference. Why are the reported standard error and confidence interval not sensible? Clicking on the
To encourage subjects to make responses on sensitive questions, the method of randomized response is often used. The subject is asked to flip a coin, in secret.If it is a head, the subject tosses the coin once more and reports the outcome, head or tails. If, instead, the first flip is a tail, the
Let π be the probability that a randomly selected voter prefers the Republican candidate. You sample two people, and neither prefers theRepublican. Find the point estimate of π. Does this estimate seem sensible? Why?(The Bayesian estimator is an alternative one that uses a subjective approach,
Find the true standard error of the sample proportion when π = 0 or π = 1. What does this reflect?
You know the sample mean ¯y of n observations.Once you know (n−1) of the observations, show that you can find the remaining one. In other words, for a given value of ¯y, the values of (n − 1) observations determine the remaining one. In summarizing scores on a quantitative variable, having
For a random sample of n subjects, explain why it is about 95% likely that the sample proportion has error no more than 1/√n in estimating the population proportion.(Hint: To show this “1/√n rule,” find two standard errors when π = 0.50, and explain how this compares to two standard errors
Refer to the previous exercise. Provide the proper interpretation.
Arandom sample of 100 records yields a 95% confidence interval for the mean age at first marriage of women in a certain country of 20.5 to 24.0 years. Explain what is wrong with each of the following interpretations of this interval.(a) If random samples of 100 records were repeatedly selected,
Based on responses of 1467 subjects in General Social Surveys, a 95% confidence interval for the mean number of close friends equals (6.8, 8.0). Which of the following interpretations is (are) correct?(a) We can be 95% confident that ¯y is between 6.8 and 8.0.(b) We can be 95% confident that μ is

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