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mathematics
statistics

John E Freunds Mathematical Statistics With Applications 8th Edition Irwin Miller, Marylees Miller - Solutions

A pediatrician speculated that frequency of visits to his office may be influenced by type of medical insurance coverage. As an exploratory study, she randomly chose 15 patients: 5 whose parents belong to a health maintenance organization (HMO), 5 whose parents had traditional medical insurance,
A high school guidance counselor hypothesized that peer group identity may have an effect on the number of schools to which her college-prep students apply. She draws eight students at random from the €œgeeks,€ the €œpunks,€ and the
A health researcher is interested in comparing three methods of weight loss: low-calorie diet, low-fat diet, and low carb diet. He selects 30 moderately overweight subjects and randomly assigns 10 to each weight-loss program. The following weight reductions (in pounds) were observed after a 1-month
1. Which is not true of parametric tests? a. They require interval data. b. They require normality in the population. c. They are less powerful than nonparametric tests. d. None of the above. 2. In a chi-square test, the expected frequencies a. are expected to occur under the terms of the null
Some recent studies have suggested that the chance of a baby being born prematurely are increased when the mother suffers from chronic oral infections such as periodontal disease. An interested researcher collected the following data. Applying Yates€™s correction, conduct a chisquare
A researcher interested in suicide created the following 2 X 2 cross-tabulation, which crosses gender with whether a suicide attempt was successfully completed. Applying Yates€™s correction, test the null hypothesis that the relative frequency of women who successfully commit suicide is
The following is a 2 Ã— 2 cross-tabulation of gender of schizophrenic patients by their responsiveness to medication. Applying Yates€™s correction, conduct a chi-square test of significance.
The following is a 2 Ã— 2 cross-tabulation of gender of juvenile violent offenders by whether they were victims of abuse before they began offending. Applying Yates€™s correction, conduct a chi-square test of significance.
The following 2 Ã— 2 cross-tabulation represents whether politicians are Republican or Democrat by whether they favor or oppose stricter gun control laws. Applying Yates€™s correction, conduct a chi-square test of significance.
The following 2 Ã— 2 cross-tabulation represents whether high school students passed the road test for their driver€™s license on the first attempt b whether they took a driver€™s education course. Applying Yates€™s correction, conduct a chi-square test of significance.
The following is a 2 Ã— 2 cross-tabulation of preference for slasher films such as Halloween or Friday the 13th by gender of respondent. Applying Yates€™s correction, conduct a chisquare test of significance.
A computer company conducted a €œnew and improved€ course designed to train its service representatives in learning to repair personal computers. One hundred trainees were split into two groups on a random bases: 50 took the customary course and 50 took the new course. At the end of 6 weeks,
Does voting behavior vary by social class? To find out, a political scientist questioned a random sample of 80 registered voters about the candidate for office, A or B, they intended to support in an upcoming election. The researcher also questioned members of her sample concerning their social
Do single-parent families tend to be more impoverished than families with two parents? A family researcher studied a sample of 35 one-parent and 65 two-parent families in a particular city to determine whether their total family income fell below the poverty level. Applying a chi-square to the
Should the Internet be censored on school computers? These days, computers and the Internet are being increasingly used in schools for all ages, and a common issue that must be addressed is whether students should have access to everything the Internet has to offer. Wondering if teachers view this
A sample of 118 college students is asked whether they are involved in campus activities. Using the following cross-tabulation depicting student responses by the region in which their colleges are located, conduct a chi-square test of significance for regional differences.
Returning to the data on the racial distribution of traffic stops from Problem 9 the researcher cross-tabulates the race of the driver with the race of the police officer for the random sample of 250 recorded stops. Note that there were too few stops by officers who are neither White nor Black to
A radio executive considering a switch in his station€™s format collects data on the radio preferences of various age groups of listeners. Using the following cross-tabulation, test the null hypothesis that radio format preference does not differ by age group.
Conduct chi-square tests of significance for the choice of murder weapon by gender of offender cross-tabulations shown in Tables 9.5 and 9.6. What is the effect of collapsing categories?
Two samples of students were asked to read and then evaluate a short story written by a new author. One-half of the students were told that the author was a woman, and the other half were told that the author was a man. The following evaluations were obtained (higher scores indicating more
A researcher concerned with racial justice suspects that jurors might perceive the severity of a crime as greater when the victim is white rather than black. She provides mock jurors with videotapes of trials (in which the victim is not shown) and arbitrarily describes the victim as either white or
How many registered voters would vote to elect a female president? A curious political scientist selected two equivalent samples of voters. One group was given the description of a hypothetical male candidate who takes the most popular stance on most major issues, while the other group was given
How many registered voters would vote to elect a female president? A curious political scientist selected two equivalent samples of voters. One group was given the description of a hypothetical male candidate who takes the most popular stance on most major issues, while the other group was given
A researcher was interested in studying the phenomenon known as social distance, the reluctance of people to associate with members of different ethnic and racial groups. She designed and experiment in which students enrolled in a lecture course were asked to choose a discussion group (all meeting
Some politicians have been known to complain about the liberal press. To determine if in fact the press is dominated by left-wing writers, a researcher assesses the political leanings of a random sample of 60 journalists. He found that 15 were conservative, 18 were moderate, and 27 were liberal.
A researcher is interested in determining if the pattern of traffic stops by the local police indicates discriminatory treatment against minorities. She takes a random sample of 250 records of traffic stops by the police, observing the racial distribution of the drivers shown in the table below.
1. When the points in a scatter plot cluster closely around the regression line, the correlation can be said to be a. weak. b. strong. c. positive. d. negative 2. When respondents who score high on the SAT’s tend also to get high grades in college, whereas those who score low on the SATs do
A psychiatrist is concerned about his daughter, who has suffered from extremely low self esteem and high anxiety since entering high school last year. Wondering if many of his daughter’s peers have the same troubles, he collects a random ample of high school girls and anonymously how much they
A new high school special education teacher wonders if there really is a correlation between reading disabilities and attention disorders. She collects data from six of her students on their reading abilities (X) and their attention abilities (Y),with a higher core indicating greater ability for
A researcher wonders if there I a correlation between (X) people’s opinions of bilingual education and (Y) their opinions about whether foreign-born citizens should e allowed to run for president. She collects the following data, with both variables being measured on a scale from 1 to 9 (1 being
Obesity in children is a major concern because t pts them at risk for several serious medical problems. Some researchers believe that a major issue related to this is that children these days spend too much time watching television and not enough time being active. Based on a sample of boys of
Is there a relationship between (X) rate of poverty (measured as percent of population below poverty level) and (Y) rates of teen pregnancy (measured per 1,000 females aged 15 to 17)? A researcher selected random states and collected the following data. Compute a Pearson€™s correlation
In preparing for a examination, some students in a class studied more than others. Each student€™s grade on the 10-point exam and the number of hours studied were as follows:Calculate a Pearson€™s correlation coefficient and determine whether the correlation is significant.
A researcher set out to determine whether suicide and homicide rates in metropolitan areas around the country are correlated and, if so, whether they vary inversely (negative correlation) or together (positive correlation). Using available data for a recent year, he compared the following sample of
An educational researcher interested in the consistency of school absenteeism over time studied a sample of 8 high school students for whom complete school records were available. The researcher counted the number of days each student had missed while in the sixth grade and then in the tenth grade.
Do reading and TV viewing compete for leisure time? To find out, a communication specialist interviewed a sample of 10 children regarding the number of books they had read during the last year and the number of hours they had spent watching TV on a daily basis. Her results are as follows:What is
The following six students were questioned regarding (X) their attitudes toward the legalization of prostitution and (Y) their attitudes toward the legalization of marijuana. Compute a Pearson€™s correlation coefficient for these data and determine whether the correlation is significant.
A high school guidance counselor is interested in the relationship between proximity to school and participation in extracurricular activities. He collects the data on distance from home to school (in miles) and number of clubs joined for a sample of 10 juniors. Using the following data, compute a
An urban sociologist interested in neighborliness collected data for a sample of 10 adults on (X) how many years they have lived in their neighborhood and (Y) how many of their neighbors they regard as friends. Compute a Pearson’s correlation coefficient for these data and determine whether the
An economist is interested in studying the relationship between length of unemployment and job-seeking activity among white-collar workers. He interviews a sample of 12 unemployed accountants as to the number of weeks they have been unemployed (X) and seeking a job during the past year (Y). Compute
1. In a regression analysis, we predict the value of Y from X based on a a. significant correlation coefficient. b. a mathematical equation. c. a weak positive correlation. d. a normal curve. 2. Which of the following denotes the slope or the regression coefficient for X? a. The Y-intercept. b. The
Crime-related television shows and movies often paint a picture in which police must go “above the law” to catch criminals, implying that to do their jobs the police must circumvent the court’s strict rules protecting offenders’ civil liberties. Do people who watch these programs come to
A researcher is interested in the association between (X) people€™s attitudes toward the war in Afghanistan and (Y) how much they support Barack Obama. In March 2009, she takes a random sample of American adults and collects the following data (both variables being measured on a scale from 1 to
Psychologist Erik Erikson suggested that individuals go through eight developmental stages throughout their lives. He believed that during stage 8 (age 65 to death), older adults will either fear or accept death depending on how much pleasure and satisfaction they feel they have experienced when
A psychiatrist wondered how much a night’s sleep could affect a person’s alertness and reaction time. She collected a random sample of people and asked them (X) how many hours of sleep they got the night before and then used a simple test to determine (Y) their reaction time in seconds. The
Does the number of years that a woman is on birth control (X) have an effect on how long it takes for her to become pregnant (Y) once she ceases to use it and tries to have children? A curious researcher collected the following data for a sample of pregnant women who had previously used birth
An educational researcher was interested in the effect of academic performance in high school on academic performance in college. She consulted the school records of 12 college graduates, all of whom had attended the same high school, to determine their high school cumulative grade average (X) and
Suppose that a researcher collected the following set of data on years of education (X) and number of children (Y) for a sample of 10 married adults: X Y 12………………. 2 14………………. 1 17………………. 0 10………………. 3 8……………….
This same researcher then selected at random one child from each of the eight families in which there was at least one child. Interested in the effects of number of siblings (X) on happiness of the child (Y) on a scale, assumed to be interval, from 1 (very unhappy) to 10 (very happy), she had these
A legal researcher wanted to measure the effect of length of a criminal trial on the length of jury deliberation. He observed in a sample of 10 randomly selected courtroom trails the following data on length of trial (in days) and length of jury deliberation (in hours).a. Draw a scatter plot of the
A personnel specialist with a large accounting firm is interested in determining the effect of seniority (the number of years with the company) on hourly wages for secretaries. She selects at random 10 secretaries and compares their years with the company (X) and hourly wages (Y): X
A communications researcher wanted to measure the effect of television viewing on aggressive behavior. He questioned a random sample of 14 children as to how many hours of television they watch daily (X) and then, as a measure of aggression, observed the number of schoolmates they physically
1. When the requirements of Pearson’s r cannot be met, we might still be able to employ a. a t ratio. b. a parametric measure of correlation. c. a nonparametric measure of correlation. d. None of the above 2. Why would we decide to test the significance of a rank-order, gamma, or
A social worker notices that some of her most anxious clients often come to see her with coffee mugs in hand. Wondering if their anxiousness (X) is related to their amount of caffeine consumption (Y), she randomly samples 10 of her clients and ranks them on both variables. The following results
An educational sociologist studied 12 college graduates €“ the entire graduating class of a small college €“ to determine whether their academic achievement as high school students was related to how well they performed in college. As shown, cumulative grade-point average in high school and
A sociologist interested in the relationship between social class and amount of reading asked a sample of 105 children from varying socioeconomic backgrounds about the number of books they had read outside of school during the last year. For the following data, compute a gamma coefficient to
A researcher was interested in whether job satisfaction is related to commuting time to work. He interviewed 185 employees of a particular company concerning their commuting time (X) and their job satisfaction (Y). For the following data, compute a gamma coefficient to determine the degree of
The following 96 students were ranked from high to low with respect to their consumption of alcoholic beverages (X) and their daily use of marijuana (Y). For these data, compute a gamma coefficient to determine the degree of association between consumption of alcohol and use of marijuana, and
A researcher is interested in determining the degree of association between the political party affiliation of husbands and wives. For the following cross-tabulation, calculate chisquare and determine the phi coefficient.
A curious graduate student wanted to determine the degree of association between successful campaign fund raising and political success in elections. The following crosstabulation displays the data she collected about the amount of fund raising and overall political success:
A researcher is interested in determining the degree of association between the political leanings of husbands and wives. For the following cross-tabulation, calculate chi-square and determine the contingency coefficient.
A medical sociologist internist is curious as to whether there is any connection between various behaviors that could be viewed as risk taking. She collects data from her records on 162 patients concerning their usage of seat belts and of cigarettes. For the following cross-tabulation, calculate
To collect evidence pertaining to gender discrimination, a sample of college professors was classified by academic rank and gender. For the following cross-tabulation, calculate chi-square and Cramer€™s V.
Does birth order influence how much a child obeys his or her parents? For the following cross-tabulation, calculate chi-square and Cramer€™s V.
A researcher collected data from 198 people about their political leaning and whether they would favor reinstating the assault weapons ban. For the following cross-tabulation, calculate chi-square and Cramer€™s V.
To find out if wealthier women tend to have Cesarean sections (C-sections) more often than poorer women, a sample of recent mothers was classified by socioeconomic status and whether they delivered their baby via C-section. For the following cross-tabulation, calculate the chi-square and
The following five students were ranked in terms of when they completed an exam (1 = first to finish, 2 = second to finish, and so on) and were given an exam grade by the instructor. Test the null hypothesis of no relationship between grade (X) and length of time to complete the exam (Y) (that is,
In Chapter 10 data were presented on the distance to school (X) and number of clubs joined (Y) for 10 high school students to which the Pearson€™s correlation coefficient was applied. One of the students (David), who previously lived 10 miles from school, has now moved farther away. He is
A medical sociologist investigated the relationship between severity of illness (X) and length of stay in a hospital (Y). Choosing eight patients at random, she ranked the seriousness of their ailment and determined the number of days they were hospitalized. Her results were as follows:Compute a
A demographer was interested in the relationship between population density (X) and quality of life (Y). Ranking 10 major cities on both variables, he obtained the following results:Compute the rank-order correlation and indicate whether there is a significant relationship between X and Y.
A researcher is interested in the relationship between political participation (X) and years of education (Y). After selecting a random sample of people over the age of 18, he ranked them in terms of their amount of political participation and determined their years of education. He obtained the
A psychology professor decides to give a quiz at the beginning of every class in hopes that it will encourage her students to do the assigned readings. However, after a few quizzes have been given, she begins to wonder if her quizzes are truly separating those students who read the material but did
An operation consists of two steps, of which the first can be made in n1 ways. If the first step is made in the ith way, the second step can be made in n2i ways. (a) Use a tree diagram to find a formula for the total number of ways in which the total operation can be made. (b) A student can study
In some problems of occupancy theory we are concerned with the number of ways in which certain indistinguishable objects can be distributed among individuals, urns, boxes, or cells with at least one in each cell. Find an expression for the number of ways in which r indistinguishable objects can be
Construct the seventh and eighth rows of Pascal’s triangle and write the binomial expansions of (x+y)6 and (x+y)7.
Substituting appropriate values for x and y into the formula of Theorem 1.9, show that(a)(b)(c)
If n is not a positive integer or zero, the binomial expansion of (1+y)n yields, for−1<y<1, the infinite seriesUse this generalized definition of binomial coefficients (which agrees with the one on page 12 for positive integral values of n) to evaluate(a)(b) √5 writing √5 = 2(1 +
With reference to the generalized definition of binomial coefficients in Exercise 1.19, show that(a)(b)
Find the coefficient of x2y3z3w in the expansion of (2x+3y−4z+w)9.
A thermostat will call for heat 0, 1, or 2 times a night. Construct a tree diagram to show that there are 10 different ways that it can turn on the furnace for a total of 6 times over 4 nights.
On August 31 there are five wild-card terms in the American League that can make it to the play-offs, and only two will win spots. Draw a tree diagram which shows the various possible play-off wild-card teams.
There are four routes, A, B, C, and D, between a person’s home and the place where he works, but route B is one-way, so he cannot take it on the way to work, and route C is one-way, so he cannot take it on the way home. (a) Draw a tree diagram showing the various ways the person can go to and
The pro at a golf course stocks two identical sets of women’s clubs, reordering at the end of each day (for delivery early the next morning) if and only if he has sold them both. Construct a tree diagram to show that if he starts on a Monday with two sets of the clubs, there are altogether eight
Suppose that in a baseball World Series (in which the winner is the first team to win four games) the National League champion leads the American League champion three games to two. Construct a tree diagram to show the number of ways in which these teams may win or lose the remaining game or games.
With reference to Exercise 1.1, suppose that there is a third step, and if the first step is made in the ith way and the second step in the jth way, the third step can be made in n3ij ways.(a) Use a tree diagram to verify that the whole operation can be made inDifferent ways.(b) With reference to
Counting the number of outcomes in games of chance has been a popular pastime for many centuries. This was of interest not only because of the gambling that was involved, but also because the outcomes of games of chance were often interpreted as divine intent. Thus, it was just about a thousand
The price of a European tour includes four stopovers to be selected from among 10 cities. In how many different ways can one plan such a tour (a) If the order of the stopovers matters; (b) If the order of the stopovers does not matter?
A carton of 15 light bulbs contains one that is defective. In how many ways can an inspector choose 3 of the bulbs and (a) Get the one that is defective; (b) Not get the one that is defective?
How many distinct permutations are there of the letters in the word “statistics”? How many of these begin and end with the letter s?
In Example 1.4 we showed that a true–false test consisting of 20 questions can be marked in 1,048,576 different ways. In how many ways can each question be marked true or false so that (a) 7 are right and 13 are wrong; (b) 10 are right and 10 are wrong; (c) At least 17 are right?
Among the seven nominees for two vacancies on a city council are three men and four women. In how many ways can these vacancies be filled (a) With any two of the seven nominees; (b) With any two of the four women; (c) With one of the men and one of the women?
A shipment of 10 television sets includes three that are defective. In how many ways can a hotel purchase four of these sets and receive at least two of the defective sets?
In a two-team basketball play-off, the winner is the first team to win m games.(a) Counting separately the number of play-offs requiring m, m+1,..., and 2m−1 games, show that the total number of different outcomes (sequences of wins and losses by one of the teams) is(b) How many different
How many different bridge hands are possible containing five spades, three diamonds, three clubs, and two hearts?
Rework Exercise 1.56 given that at least two of the cans of tennis balls were sold on each of the three days. In exercise On a Friday morning, the pro shop of a tennis club has 14 identical cans of tennis balls. If they are all sold by Sunday night and we are interested only in how many were sold
When n is large, n! can be approximated by means of the expressionCalled Stirling’s formula, where e is the base of natural logarithms. (A derivation of this formula may be found in the book by W. Feller cited among the references at the end of this chapter.)(a) Use Stirling’s formula to obtain
Using Stirling’s formula (see Exercise 1.6) to approximate 2n! and n!, show that
Use Venn diagrams to verify that (a) (A ∪ B). C is the same event as A ∪ (B ∪ C); (b) A ∩(B ∪ C) is the same event as (A ∩ B) ∪ (A ∩ C);
A department store that bills its charge- account customers once a month has found that if a customer pays promptly one month, the probability is 0.90 that he or she will also pay promptly the next month; however, if a customer does not pay promptly one month, the probability that he or she will
With reference to Figure 2.15, verify that events A, B, C, And D are independent. The region rep-resenting A consists of two circles, And so do the regions representing B And C.Figure 2.15

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