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mathematics
statistics

Questions and Answers of Statistics

Consider a multinomial experiment involving n = 150 trials and k = 4 cells. The observed frequencies resulting from the experiment are shown in the accompanying table, and the null hypothesis to be
For Exercise, retest the hypotheses, assuming that the experiment involved twice as many trials (n = 300) and that the observed frequencies were twice as high as before, as shownhere.
The results of a multinomial experiment with k = 5 were recorded. Each outcome is identified by the numbers 1 to 5. Test to determine whether there is enough evidence to infer that the proportions of
A multinomial experiment was conducted with k = 4. Each outcome is stored as an integer from 1 to 4 and the results of a survey were recorded. Test the following hypotheses.H0: p1 = .15, p2 = .40, p3
To determine whether a single die is balanced, or fair, the die was rolled 600 times. Is there sufficient evidence to allow you to conclude that the die is not fair? Discuss.
Grades assigned by an economics instructor have historically followed a symmetrical distribution: 5% A’s, 25% B’s, 40% C’s, 25% D’s and 5% F’s. This year, a sample of 150 grades was
Pat Statsdud is about to write a multiple-choice exam but as usual knows absolutely nothing. Pat plans to guess one of the five choices. Pat has been given one of the professor’s previous exams
Financial managers are interested in the speed with which customers who make purchases on credit pay their bills. In addition to calculating the average number of days that unpaid bills (called
License records in a county reveal that 15% of cars are subcompacts (1), 25% are compacts (2), 40% are midsize (3), and the rest are an assortment of other styles and models (4). A random sample of
In an election held last year that was contested by three parties. Party A captured 31% of the vote, party B garnered 51%, and party C received the remaining votes. A survey of 1,200 voters asked
In a number of pharmaceutical studies volunteers who take placebos (but are told they have taken a cold remedy) report the following side effects:Headache (1) ............5%Drowsiness (2)
Refer to Exercise, where the statistics practitioner estimated the size of market segments based on education among California adults. Suppose that census figures from 10 years ago showed the
According to the Statistical Abstract of the United States 2012, Table 56, the proportions for each category of marital status in 2007 was:Never married (including partnered, not married)
Test to determine whether there is sufficient evidence that the General Social Survey in 2012 overrepresented at least one race (RACE).According to the Statistical Abstract of the United States 2012,
Is there sufficient evidence to conclude that the General Social Survey in 2010 overrepresented at least one race (RACE)?According to the Statistical Abstract of the United States 2012, Table 56, the
Can we infer that the General Social Survey in 2012 overrepresented at least one category of marital status (MARITAL)?
Is there sufficient evidence to conclude that the General Social Survey in 2010 overrepresented at least one category of marital status (MARITAL)?
Conduct a test to determine whether the two classifications L and M are independent, using the data in the accompanying cross-classification table. (Use Î± =.05.)
Repeat Exercise using the followingtable:
Repeat Exercise using the following table:Review the results of Exercises. What is the effect of decreasing the samplesize?
Conduct a test to determine whether the two classifications R and C are independent, using the data in the accompanying cross-classification table. (Use Î± = .10.)ApplicationsUse a 5% significance
The trustee of a companyâ€™s pension plan has solicited the opinions of a sample of the companyâ€™s employees about a proposed revision of the plan.AÂ breakdown of the responses is
The operations manager of a company that manufactures shirts wants to determine whether there are differences in the quality of workmanship among the three daily shifts. She randomly selects 600
One of the issues that came up in a recent national election (and is likely to arise in many future elections) is how to deal with a sluggish economy. Specifically, should governments cut spending,
Econetics Research Corporation, a well-known Montreal-based consulting firm, wants to test how it can influence the proportion of questionnaires returned from surveys. In the belief that the
A major North American city has four competing newspapers: the Globe and Mail (G&M), Post, Sun, and Star. To help design advertising campaigns, the advertising managers of the newspapers need to
An investor who can correctly forecast the direction and size of changes in foreign currency exchange rates is able to reap huge profits in the international currency markets. A knowledgeable reader
Is there brand loyalty among car owners in their purchases of gasoline? To help answer the question, a random sample of car owners was asked to record the brand of gasoline in their last two
During the past decade, many cigarette smokers have attempted to quit. Unfortunately, nicotine is highly addictive. Smokers use a large number of different methods to help them quit. These include
Because television audiences of newscasts tend to be older (and because older people suffer from a variety of medical ailments), pharmaceutical companies’ advertising often appears on national news
The associate dean of a business school was looking for ways to improve the quality of the applicants to its MBA program. In particular, she wanted to know whether the undergraduate degree of
The relationship between drug companies and medical researchers is under scrutiny because of possible conflict of interest. The issue that started the controversy was a 1995 case control study that
After a thorough analysis of the market, a publisher of business and economics statistics books has divided the market into three general approaches to teach applied statistics. These are (1) use of
Every year, there are more than 300,000 robberies in the United States. A researcher took a random sample of robberies in 2000, 2005, and 2010, and recorded the weapon used (1 = Firearm, 2 = Knife or
Refer to Exercise. The engineering team took samples of bridges in 2004, 2006, 2008, and 2010 and recorded whether each bridge was structurally deficient, functionally obsolete, or structurally
Household types are categorized in the following way: 1. Married couples with children, 2. Married couples without children, 3. Single parent, 4. One person, 5. Other. Random samples of families
Refer to Exercise. Random samples from Denmark, Ireland, the Netherlands, and Sweden were drawn. Is the sufficient evidence to infer that there are differences in household types between the four
A statistics practitioner took random samples from Canada, Australia, New Zealand, and the United Kingdom, and classified each person as either obese (2) or not (1). Can we conclude from these data
To measure the extent of cigarette smoking around the world, random samples of adults in Denmark, Finland, Norway, and Sweden were drawn. Each was asked whether he or she smoked (2 = Yes, 1 = No).
Refer to Exercise. The survey was performed in Canada, Australia, New Zealand, and the United Kingdom. Is there enough evidence to infer that there are differences in adult cigarette smoking between
In 2013, the Supreme Court of the United States ruled on a California law that banned same-sex marriage. An important element of that decision was public opinion. In March, Public Policy Polling
An important element in the business of politics is to know who supports you and who doesn’t. Is there sufficient evidence to infer that men and women (SEX: 1 = Male, 2 = Female) differ in their
Do foreign-born Americans differ from Americans born in the United States (BORN: 1 = Born in the U.S., 2 = Born elsewhere) in their support of political groups (PARTYID3: 1 = Democrat, 2 =
Is it a myth that men are more conservative and women more liberal? Conduct a test to determine if men and women (SEX: 1 = Male, 2 = Female) differ in their political views (POLVIEWS3: 1 = Liberal, 2
Do Americans who work for themselves (WRKSLF: 1 = Self-employed, 2 = Someone else) support the same political groups (PARTYID3: 1 = Democrat, 2 = Independent, 3 = Republican) as Americans who work
Are government workers more or less conservative than people who work in the private sector? Is there sufficient evidence to conclude that government workers (WRKGOVT: 1 = Government, 2 = Someone
The issue of gun control in the United States is one that often debated particularly during elections. The question arises, what does the public think about the issue and does support vary from year
In the last two decades, an increasing proportion of women have entered the workforce. Determine whether there is enough evidence to conclude that men and women (SEX) differ in their work status
Is there sufficient evidence to infer that sup-port for capital punishment (CAPPUN: 1 = Favor, 2 = Oppose) is related to political affiliation (PARTYID3: 1 = Democrat, 2 = Republican, 3 =
Know where to vote (KNOW)Excel users should note that any row containing one or two empty cells must be removed. Use a 5% significance level. For each of the following variables, conduct a test to
Read about campaign in newspaperExcel users should note that any row containing one or two empty cells must be removed. Use a 5% significance level. For each of the following variables, conduct a
Have health insurance (HEALTH)Excel users should note that any row containing one or two empty cells must be removed. Use a 5% significance level. For each of the following variables, conduct a test
Have access to the Internet (ACCESS)Excel users should note that any row containing one or two empty cells must be removed. Use a 5% significance level. For each of the following variables, conduct a
Suppose that a random sample of 100 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in
A random sample of 50 observations yielded the following frequencies for the standardized intervals:Interval FrequencyZ ≤ −1.............. 6−1 < Z ≤ 0 ...........270 < Z ≤ 1
Refer to Exercise. Test at the 10% significance level to determine whether the amount of time spent working at part-time jobs is normally distributed. If there is evidence of nonnormality, is the
The t-test in Exercise requires that the costs of prescriptions is normally distributed. Conduct a test with α = .05 to determine whether the required condition is unsatisfied. If there is enough
Exercise required you to conduct a t-test of the difference between two means. Each samples productivity data are required to be normally distributed. Is that required condition violated? Test with
Exercise asked you to conduct a t-test of the difference between two means (reaction times). Test to determine whether there is enough evidence to infer that the reaction times are not normally
In Exercise, you performed a test of the mean matched pairs difference. Test with a 10% significance level to determine whether the normality requirement is violated.
An organization dedicated to ensuring fairness in television game shows is investigating Wheel of Fortune. In this show, three contestants are required to solve puzzles by selecting letters. Each
It has been estimated that employee absenteeism costs North American companies more than $100 billion per year. As a first step in addressing the rising cost of absenteeism, the personnel department
Suppose that the personnel department in Exercise continued its investigation by categorizing absentees according to the shift on which they worked, as shown in the accompanying table. Is there
A management behavior analyst has been studying the relationship between male/female supervisory structures in the workplace and the level of employeesâ€™ job satisfaction. The results of a
Stress is a serious medical problem that costs businesses and government billions of dollars annually. As a result, it is important to determine the causes and possible cures. It would be helpful to
More than 3,000 Americans quit smoking each day. Because nicotine is one of the most addictive drugs, quitting smoking is a difficult and frustrating task. It usually takes several tries before
A newspaper publisher trying to pinpoint his market’s characteristics wondered whether the way people read a newspaper is related to the reader’s educational level. A survey asked adult readers
Every week, the Florida Lottery draws six numbers between 1 and 49. Lottery ticket buyers are naturally interested in whether certain numbers are drawn more frequently than others. To assist players,
A scientist believes that the gender of a child is a binomial random variable with probability = .5 for a boy and .5 for a girl. To help test her belief, she randomly samples 100 families with five
Given the high cost of medical care, research that points the way to avoid illness is welcome. Previously performed research tells us that stress affects the immune system. Two scientists at Carnegie
Exercise described the problem of a looming shortage of professors, possibly made worse by professors desiring to retire before the age of 65. A survey asked a random sample of professors whether he
Refer to Exercise. Determine whether there is enough evidence to infer that there are differences in the choice of Christmas tree between the three age categories.
Exercise described a study to determine whether viewers (older than 50) of the network news had contacted their physician to ask about one of the prescription drugs advertised during the newscast.
Exercise described a survey of adults wherein, on the basis of several probing questions, each was classified as either a member of the health conscious group (code = 1) or not (code = 2) and whether
Example, described exit polls wherein people are asked whether they voted for the Democrat or Republican candidate for president.The surveyors also record gender (1 = Female, 2 = Male), educational
Exercise described the market segments defined by JC Penney. Another question included in the questionnaire that classified the women surveyed was asked whether each worked outside the home. The
Refer to Exercise. The women in the survey were also asked to define value by identifying what they considered to be the most important attribute of value. The responses are:1. Price2. Quality3.
Refer to Example, In segmenting the breakfast cereal market, a food manufacturer uses health and diet consciousness as the segmentation variable. Four segments are developed:1. Concerned about eating
An analysis of the applicants of all MBA programs in North America reveals that the proportions of each type of undergraduate degree are as follows:Under Graduate Degree ……
The experiment to determine the effect of taking a preparatory course to improve SAT scores in Exercise A13.16 was criticized by other statisticians. They argued that the first test would provide a
How does dieting affect the brain? This question was addressed by researchers in Australia. The experiment used 40 middle-age women in Adelaide, Australia; half were on a diet and half were not
A small but important part of a university library’s budget is the amount collected in fines on overdue books. Last year, a library collected $75,652.75 in fine payments; however, the head
An apple juice manufacturer has developed a new product—a liquid concentrate that produces 1 liter of apple juice when mixed with water. The product has several attractive features. First, it is
Mutual funds are a popular way of investing in the stock market. A financial analyst wanted to determine the effect income had on ownership of mutual funds and whether the relationship had changed
Refer to Exercise A15.5. Suppose that in addition to varying the marketing strategy, the manufacturer also decided to advertise in one of the two media that are available: television and newspapers.
After a recent study, researchers reported on the effects of folic acid on the occurrence of spina bifida—a birth defect in which there is incomplete formation of the spine. A sample of 2,000 women
Slow play of golfers is a serious problem for golf clubs. Slow play results in fewer rounds of golf and less profits for public course owners. To examine this problem, a random sample of
The United States and Canada (among others) are countries in which a significant proportion of citizens are immigrants. Many arrive in North America with few assets but quickly adapt to a changed
During the decade of the 1980s, professional baseball thrived in North America. However, in the 1990s attendance dropped, and the number of television viewers also decreased. To examine the
In an attempt to learn more about traffic congestion in a large North American city, the number of cars passing through intersections was determined (National Post, October 18, 2006). The number of
Organizations that sponsor various leisure activities need to know the number of people who wish to participate. Bureaucrats need to know the number because many organizations apply for government
Low back pain is a common medical problem that sometimes results in disability and absence from work. Any method of treatment that decreases absence would be welcome by individuals and insurance
Clinical depression is a serious and sometimes debilitating disease. It is often treated by antidepressants such as Prozac and Zoloft. Recent studies may indicate another possible remedy. Researchers
How well do airlines keep to their schedules? To help answer this question, an economist conducted a survey of 780 takeoffs in the United States and determined that 77.4% of them departed on time
During 2008, the United States was in the throes of a deep recession. The unemployment rate rose sharply. How did this affect job tenure (the amount of time a worker has been with his or her current
Capital punishment for murderers exists in most U.S. states. However, a few states ban this form of punishment. Politicians often need to know which members of the public support and which oppose.
Are married couples postponing bearing children? One way to measure this is to determine how old people are when their first child is born. Estimate with 95% confidence the average age of Americans
In Chapter 2, we used a graphical technique and data from the American National Election Survey to attempt to determine whether men and women differ in their political affiliation. Use a suitable
Do teenage and adult children living with their parents contribute to household income by holding down full- or part-time jobs? And is it more likely that they do so for affluent than for less
A generally accepted method of finding whether Americans have improved financially over a multiyear period is to calculate inflation-adjusted incomes. Using the General Social Survey data, can we

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