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statistics
elementary statistics in social research
Questions and Answers of
Elementary Statistics In Social Research
Each year, Forbes and the Center for College Affordability and Productivity (CCAP) release a list of the best colleges in the United States. Over 600 colleges and universities are ranked according to
You want to compare the numbers of crimes reported in three police precincts in a city. To do so, you randomly select 10 weeks for each precinct and record the numbers of crimes reported. The table
What are the conditions for using a Kruskal-Wallis test?
Explain why the Kruskal-Wallis test is always a right-tailed test.
The table shows the annual premiums for a random sample of home insurance policies in Connecticut, Massachusetts, and Virginia. At \(\alpha=0.05\), can you conclude that the distribution of the
A researcher wants to determine whether there is a difference in the hourly pay rates for registered nurses in Indiana, Kentucky, and Ohio. The researcher randomly selects several registered nurses
The table shows the annual salaries for a random sample of private industry workers in Kentucky, North Carolina, South Carolina, and West Virginia. At \(\alpha=0.10\), can you conclude that the
The table shows the amounts of caffeine (in milligrams) in 16-ounce servings for a random sample of beverages. At \(\alpha=0.01\), can you conclude that the distribution of the amounts of caffeine in
An insurance underwriter claims that the number of days patients spend in the hospital is different in at least one region of the United States. The table shows the numbers of days randomly selected
The table shows the energy consumed (in millions of Btu) in one year for a random sample of households from four U.S. regions. At \(\alpha=0.01\), can you conclude that the energy consumed is
The table shows the school enrollments of males and females for a random sample of 10 colleges. At \(\alpha=0.05\), can you conclude that there is a significant correlation between the number of
What are some advantages of the Spearman rank correlation coefficient over the Pearson correlation coefficient?
Describe the ranges of the Spearman rank correlation coefficient and the Pearson correlation coefficient.
What does it mean when \(r_{s}\) is equal to 1 ? What does it mean when \(r_{s}\) is equal to -1 ? What does it mean when \(r_{s}\) is equal to 0 ?
Explain, in your own words, what \(r_{s}\) and \(ho_{s}\) represent in Example 1.
In an agricultural report, a commodities analyst claims that there is a significant correlation between purchased seed expenses and fertilizer and lime expenses in the farming business. The table
The table shows the overall scores and the prices for a random sample of nine different models of elliptical exercise machines. The overall score represents the ergonomics, exercise range, ease of
The table shows the prices (in dollars per bushel) received for barley and corn for a random sample of nine U.S. farmers. At \(\alpha=0.05\), can you conclude that there is a significant correlation
Vacuum Cleaners The table shows the overall scores and the prices for a random sample of 12 different models of vacuum cleaners. The overall score represents cleaning, airflow, handling, noise, and
At \(\alpha=0.10\), can you conclude that there is a significant correlation between science achievement scores and GNI?Use the table below. The table shows the average achievement scores of
At \(\alpha=0.10\), can you conclude that there is a significant correlation between mathematics achievement scores and GNI?Use the table below. The table shows the average achievement scores of
At \(\alpha=0.10\), can you conclude that there is a significant correlation between science and mathematics achievement scores?Use the table below. The table shows the average achievement scores of
Use the results from Exercises \(9-11\) to write a summary about the correlation (or lack of correlation) between test scores and GNI.Use the table below. The table shows the average achievement
The table shows the average hours worked per week and the numbers of on-the-job injuries for a random sample of U.S. companies in a recent year. At \(\alpha=0.10\), can you conclude that there is a
The table shows the average hours worked per week and the numbers of on-the-job injuries for a random sample of U.S. construction companies in a recent year. At \(\alpha=0.05\), can you conclude that
A liquid-dispensing machine has been designed to fill one-liter bottles. A quality control inspector decides whether each bottle is filled to an acceptable level and passes inspection \((P)\) or
As people enter a concert, an usher records where they are sitting. The results for 13 people are shown, where \(L\) represents a lawn seat and \(P\) represents a pavilion seat. At \(\alpha=0.05\),
You want to determine whether the selection of recently hired employees in a large company is random with respect to gender. The genders of 36 recently hired employees are shown below, where \(F\)
In your own words, explain why the hypothesis test discussed in this section is called the runs test.
Describe the test statistic for the runs test when the sample sizes \(n_{1}\) and \(n_{2}\) are less than or equal to 20 and when either \(n_{1}\) or \(n_{2}\) is greater than 20 .
\(T F T F T T T F F F T F\)Determine the number of runs in the sequence. Then find the length of each run.
\(U U D D U D U U D D U D U\)Determine the number of runs in the sequence. Then find the length of each run.
\(M F M F M F F F F F F M M M F F M M M M\)Determine the number of runs in the sequence. Then find the length of each run.
\(A A A B B B A B B A A A A A A B A A B A B B\)Determine the number of runs in the sequence. Then find the length of each run.
Find the values of \(n_{1}\) and \(n_{2}\) in Exercise 3.Data from Exercises 3\(T F T F T T T F F F T F\)Determine the number of runs in the sequence. Then find the length of each run.
Find the values of \(n_{1}\) and \(n_{2}\) in Exercise 4 .Data from Exercises 4\(U U D D U D U U D D U D U\)Determine the number of runs in the sequence. Then find the length of each run.
Find the values of \(n_{1}\) and \(n_{2}\) in Exercise 5 .Data from Exercises 5\(M F M F M F F F F F F M M M F F M M M M\)Determine the number of runs in the sequence. Then find the length of each
Find the values of \(n_{1}\) and \(n_{2}\) in Exercise 6 .Data from Exercises 6\(A A A B B B A B B A A A A A A B A A B A B B\)Determine the number of runs in the sequence. Then find the length of
T F T F T F T F T F T F Use the sequence and Table 12 in Appendix B to determine the number of runs that are considered too high and the number of runs that are considered too low for the data to be
\(M F M M M M M M F F M M\)Use the sequence and Table 12 in Appendix B to determine the number of runs that are considered too high and the number of runs that are considered too low for the data to
\(N S S S N N N N S N S N S S N N N\)Use the sequence and Table 12 in Appendix B to determine the number of runs that are considered too high and the number of runs that are considered too low for
\(X X X X X X X Y Y Y Y Y Y Y Y Y Y Y Y Y Y\)Use the sequence and Table 12 in Appendix B to determine the number of runs that are considered too high and the number of runs that are considered too
A coach records the results of the coin toss at the beginning of each football game for a season. The results are shown, where \(H\) represents heads and \(T\) represents tails. The coach claimed the
The sequence shows the majority party of the U.S. Senate after each election for a recent group of years, where \(R\) represents the Republican party and \(D\) represents the Democratic party. Can
The sequence shows the Major League Baseball league of each World Series winning team from 1969 to 2016, where \(N\) represents the National League and \(A\) represents the American League. Can you
A number generator outputs the sequence of digits shown, where \(O\) represents an odd digit and \(E\) represents an even digit. Test the claim that the digits were not randomly generated.(a)
A team of veterinarians record, in order, the genders of every dog that is microchipped at their pet hospital in one month. The genders of recently microchipped dogs are shown, where \(F\) represents
A golf tournament official records whether each past winner is American-born \((A)\) or foreign-born \((F)\). The results are shown for every year the tournament has existed. Can you conclude that
The sequence shows the daily high temperatures (in degrees Fahrenheit) for a city during the month of July. Test the claim that the daily high temperatures do not occur randomly.Use the following
Exam Scores The sequence shows the exam scores of a class based on the order in which the students finished the test. Test the claim that the scores occur randomly.Use the following information to
Use technology to generate a sequence of 30 numbers from 1 to 99 , inclusive. Test the claim that the sequence of numbers is not random.Use the following information to perform a runs test. You can
Before you could perform many of the hypothesis tests you learned about in previous chapters, you had to ensure that certain conditions about the population were satisfied. For instance, before you
A store manager claims that the median number of customers per day is no more than 650 . The numbers of customers per day for 17 randomly selected days are listed below. At \(\alpha=0.01\), can you
A company claims that the median credit score for U.S. adults is at least 710 . The credit scores for 13 randomly selected U.S. adults are listed below. At \(\alpha=0.05\), can you reject the
A government agency claims that the median sentence length for all federal prisoners is 2 years. In a random sample of 180 federal prisoners, 65 have sentence lengths that are less than 2 years, 109
In a study testing the effects of calcium supplements on blood pressure in men, 10 randomly selected men were given a calcium supplement for 12 weeks. The table shows the measurements for each
In a study testing the effects of an herbal supplement on blood pressure in men, 11 randomly selected men were given an herbal supplement for 12 weeks. The table shows the measurements for each
An association claims that the median annual salary of lawyers is \(\$ 118,160\). In a random sample of 125 lawyers, 76 were paid less than \(\$ 118,160\), and 49 were paid more than \(\$ 118,160\).
A career placement advisor claims that there is a difference in the total times required to earn a doctorate degree by female and male graduate students. The table shows the total times (in years) to
A medical researcher claims that a new drug affects the number of headache hours experienced by headache sufferers. The numbers of headache hours (per day) experienced by eight randomly selected
The table shows the ages for a random sample of doctorate recipients in three fields of study. At \(\alpha=0.01\), can you conclude that the distribution of the ages of the doctorate recipients in at
The table shows the starting salaries for a random sample of college graduates in four fields of engineering. At \(\alpha=0.05\), can you conclude that the distribution of the starting salaries in at
The table shows the overall scores and the prices for six randomly selected video disk players. The overall score is based mainly on picture quality. At \(\alpha=0.10\), can you conclude that there
The table shows the overall scores and the prices per gallon for seven randomly selected interior paints. The overall score represents hiding, surface smoothness, and resistance to staining,
A highway patrol officer stops speeding vehicles on an interstate highway. The genders of the last 25 drivers who were stopped are shown, where \(F\) represents a female driver and \(M\) represents a
The sequence shows the departure status of the last 18 buses to leave a bus station, where \(T\) represents a bus that departed on time and \(L\) represents a bus that departed late. Can you conclude
An organization claims that the median number of annual volunteer hours is 52. In a random sample of 75 people who volunteered last year, 47 volunteered for less than 52 hours, 23 volunteered for
A labor organization claims that there is a difference in the hourly earnings of union workers and nonunion workers in state and local governments. The table shows the hourly earnings (in dollars)
The table shows the sales prices for a random sample of apartment condominiums and cooperatives in four U.S. regions. At \(\alpha=0.01\), can you conclude that the distribution of the sales prices in
The table shows the numbers of emails sent and the numbers of emails received in a week for a random sample of nine people. At \(\alpha=0.01\), can you conclude that there is a significant
A meteorologist wants to determine whether days with rain occur randomly in April in his hometown. To do so, the meteorologist records whether it rains for each day in April. The results are shown,
The mayor called on council members at a town meeting in the sequence shown, where \(R\) represents a Republican council member and \(D\) represents a Democrat council member. At \(\alpha=0.05\), can
An employment agency representative wants to determine whether there is a difference in the annual household incomes in four regions of the United States. The representative randomly selects several
An investment company claims that the median age of people with mutual funds is 51 years. The ages (in years) of 20 randomly selected mutual fund owners are listed below. At \(\alpha=0.01\), is there
An employment agency claims that there is a difference in the weekly earnings of workers who are union members and workers who are not union members. The table shows the weekly earnings (in dollars)
The table shows the overall scores and the prices for a random sample of eight different suitcases. The overall score represents the ease of use, features, construction, and durability of a suitcase.
In a recent year, according to the Bureau of Labor Statistics, the median number of years that wage and salary workers had been with their current employer (called employee tenure) was 4.2 years.
The National Bureau of Economic Research (NBER) is a private, nonprofit, nonpartisan research organization. The NBER provides information for better understanding of how the U.S. economy works.
The heights (in inches) of 12 randomly selected current National Basketball Association players are listed. Use technology to construct a normal probability plot to determine whether the data come
In a normal probability plot, what is usually plotted along the horizontal axis? What is usually plotted along the vertical axis?
Use the histogram and normal probability plot to determine whether the data come from a normal distribution.Explain your reasoning. Frequency 25 20 20 15 10 5 Roller Coaster Heights Height (in feet)
Use the histogram and normal probability plot to determine whether the data come from a normal distribution.Explain your reasoning. Relative frequency 0.25 0.20 0.15 0.10 0.05 34.5- 35.5- 36.5- 37.5-
A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. The table shows the scores of 10 golfers while using the old design and
The table shows the earnings (in thousands of dollars) of a random sample of 10 male and 12 female pharmaceutical sales representatives. At \(\alpha=0.10\), can you conclude that there is a
One-Way Analysis of Variance (ANOVA) ANOVA can help you make important decisions about the allocation of resources. For instance, suppose you work for a large manufacturing company and part of your
Fraud.org was created by the National Consumers League (NCL) to combat the growing problem of telemarketing and Internet fraud by improving prevention and enforcement. NCL works to protect and
The Illinois State Board of Education conducts an annual study of the salaries of Illinois teachers. The study looks at how teachers' salaries are distributed based on factors such as degree and
The table below shows the winning times (in seconds) for the men's and women's 100-meter runs in the Summer Olympics from 1928 to 2016.(a) Display the data in a scatter plot, calculate the
The table at the right shows the residential natural gas expenditures (in dollars) in one year for a random sample of households in four regions of the United States. Assume that the populations are
The equation used to predict the annual sweet potato yield (in pounds per acre) is \(\hat{y}=16,212-0.227 x_{1}+0.212 x_{2}\), where \(x_{1}\) is the number of acres planted and \(x_{2}\) is the
A school administrator claims that the standard deviations of reading test scores for eighth-grade students are the same in Colorado and Utah. A random sample of 16 test scores from Colorado has a
A researcher claims that the credit card debts of college students are distributed as shown in the pie chart. You randomly select 900 college students and record the credit card debt of each. The
The contingency table shows how a random sample of adults rated a newly released movie and gender. At \(\alpha=0.05\), can you conclude that the adults' ratings are related to gender? Rating Gender
The table shows the metacarpal bone lengths (in centimeters) and the heights (in centimeters) of 12 adults. The equation of the regression line is \(\hat{y}=1.707 x+94.380\). Metacarpal 45 51 39 41
A website administrator for a company claims that the median number of visitors per day to the company’s website is no more than 1500. An employee doubts the accuracy of this claim. The numbers of
An organization claims that the median annual attendance for museums in the United States is at least 39,000. A random sample of 125 museums reveals that the annual attendances for 79 museums were
A psychologist claims that the number of repeat offenders will decrease when first-time offenders complete a particular rehabilitation course. You randomly select 10 prisons and record the number of
What is a nonparametric test? How does a nonparametric test differ from a parametric test? What are the advantages and disadvantages of using a nonparametric test?
When the sign test is used, what population parameter is being tested?
Describe the test statistic for the sign test when the sample size \(n\) is less than or equal to 25 and when \(n\) is greater than 25 .
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