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statistics
elementary statistics in social research

Questions and Answers of Elementary Statistics In Social Research

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 .
In your own words, explain why the hypothesis test discussed in this section is called the sign test.
Explain how to use the sign test to test a population median.
List the two conditions that must be met in order to use the paired-sample sign test.
A financial service accountant claims that the median credit card balance of college students is more than \(\$ 300\). You randomly select the credit card accounts of 12 college students and record
A meteorologist claims that the median daily high temperature for the month of July in Pittsburgh is \(83^{\circ}\) Fahrenheit. The high temperatures (in degrees Fahrenheit) for 15 randomly selected
A real estate agent claims that the median sales price of new privately owned one-family homes sold in a recent month is \(\$ 253,000\) or less. The sales prices (in dollars) of 10 randomly selected
During a weather report, a meteorologist claims that the median daily high temperature for the month of January in San Diego is \(66^{\circ}\) Fahrenheit. The high temperatures (in degrees
A financial services institution claims that the median amount of credit card debt for families holding such debts is at least \(\$ 2300\). In a random sample of 104 families with credit card debt,
A financial services accountant claims that the median amount of financial debt for families holding such debts is less than \(\$ 60,000\). In a random sample of 70 families with financial debt, the
A research group claims that the median age of the users of a social media website is greater than 30 years old. In a random sample of 24 users, 11 are less than 30 years old, 10 are more than 30
A research group claims that the median age of the users of a social networking website is less than 32 years old. In a random sample of 20 users, 5 are less than 32 years old, 13 are more than 32
A renters' organization claims that the median number of rooms in renter-occupied units is four. You randomly select 120 renter-occupied units and obtain the results shown below. At \(\alpha=0.05\),
A renters' organization claims that the median square footage of renter-occupied units is 1000 square feet. You randomly select 22 renter-occupied units and obtain the results shown above. At
A labor organization claims that the median hourly wage of computer systems analysts is \(\$ 41.93\). In a random sample of 45 computer systems analysts, 18 earn less than \(\$ 41.93\) per hour, 25
A labor organization claims that the median hourly wage of podiatrists is at least \(\$ 60.01\). In a random sample of 23 podiatrists, 17 earn less than \(\$ 60.01\) per hour, 5 earn more than \(\$
A physician claims that lower back pain intensity scores will decrease after receiving acupuncture treatment. The table shows the lower back pain intensity scores for eight patients before and after
A physician claims that lower back pain intensity scores will decrease after taking anti-inflammatory drugs. The table shows the lower back pain intensity scores for 12 patients before and after
A tutoring agency claims that by completing a special course, students will improve their math SAT scores. In part of a study, 12 students take the math part of the SAT, complete the special course,
A guidance counselor claims that students who take the SAT twice will improve their scores the second time they take the SAT. The table shows both math SAT scores for 12 students who took the SAT
A research organization conducts a survey by randomly selecting adults and asking each, "How do you feel relative to your age?" The results are shown in the figure.(a) Use a sign test to test the
A research organization conducts a survey by randomly selecting adults and asking each, "How frequently do you contact your parents by phone?" The results are shown in the figure. (a) Use a sign
A labor organization claims that the median weekly earnings of female workers is less than or equal to \(\$ 765\). To test this claim, you randomly select 50 female workers and ask each to provide
A labor organization claims that the median weekly earnings of male workers is greater than \(\$ 950\). To test this claim, you randomly select 70 male workers and ask each to provide his weekly
A marriage counselor claims that the median age of brides at the time of their first marriage is less than or equal to 27 years old. In a random sample of 65 brides, 24 are less than 27 years old, 35
A marriage counselor claims that the median age of grooms at the time of their first marriage is greater than 28 years old. In a random sample of 56 grooms, 33 are less than 28 years old and 23 are
How do you know whether to use a Wilcoxon signed-rank test or a Wilcoxon rank sum test?
What is the requirement for the sample size of each sample when using the Wilcoxon rank sum test?
In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium supplement for 12 weeks. The table shows the measurements for each
A private industry analyst claims that there is no difference in the salaries earned by workers in the wholesale trade and manufacturing industries. The table shows the salaries (in thousands of
A college administrator claims that there is a difference in the earnings of people with bachelor's degrees and those with advanced degrees. The table shows the earnings (in thousands of dollars) of
A medical researcher wants to determine whether a new drug affects the number of headache hours experienced by headache sufferers. To do so, the researcher randomly selects seven patients and asks
A teacher's union representative claims that there is a difference in the salaries earned by teachers in Wisconsin and Michigan. The table shows the salaries (in thousands of dollars) of a random
A physician wants to determine whether an experimental medication affects an individual's heart rate. The physician randomly selects 15 patients and measures the heart rate of each. The subjects then
A petroleum engineer wants to know whether a certain fuel additive improves a car's gas mileage. To decide, the engineer records the gas mileages (in miles per gallon) of 33 randomly selected cars
A petroleum engineer claims that a fuel additive improves gas mileage. The table shows the gas mileages (in miles per gallon) of 32 randomly selected cars measured with and without the fuel additive.
Correlation and Regression Correlation and regression analysis can be used to determine whether there is a significant relationship between two variables. When there is, you can use one of the
The equation used to predict the net sales (in millions of dollars) for a fiscal year for a clothing retailer is\[ \hat{y}=23,769+9.18 x_{1}-8.41 x_{2} \]where \(x_{1}\) is the number of stores open
Calculate the correlation coefficient \(r\) and interpret the result.Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary
Test the significance of the correlation coefficient \(r\) that you found in Exercise 3.Use \(\alpha=0.01\).Use the data in the table, which shows the average annual salaries (both in thousands of
Find the equation of the regression line for the data. Draw the regression line on the scatter plot that you constructed in Exercise 2.Use the data in the table, which shows the average annual
Use the regression equation that you found in Exercise 5 to predict the average annual salary of postsecondary library science teachers when the average annual salary of librarians is \(\$
Find the coefficient of determination \(r^{2}\) and interpret the result.Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and
Find the standard error of estimate \(s_{e}\) and interpret the result.Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and
Construct a \(99 \%\) prediction interval for the average annual salary of postsecondary library science teachers when the average annual salary of librarians is \(\$ 56,000\). Interpret the
Acid rain affects the environment by increasing the acidity of lakes and streams to dangerous levels, damaging trees and soil, accelerating the decay of building materials and paint, and destroying
The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Under FDA regulations, manufacturers are required to list the amounts of certain nutrients in their foods, such
A tax preparation company randomly selects 300 adults and asks them how they prepare their taxes. The results are shown at the right. Find the observed frequency and the expected frequency (using the
A retail trade association claims that the tax preparation methods of adults are distributed as shown in the table at the left below. A tax preparation company randomly selects 300 adults and asks

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