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statistics
elementary statistics in social research

Questions and Answers of Elementary Statistics In Social Research

A researcher claims that the number of different-colored candies in bags of dark chocolate M&M’s® is uniformly distributed. To test this claim, you randomly select a bag that contains 500 dark
\(n=125, p_{i}=0.4\)Find the expected frequency for the values of \(n\) and \(p_{i}\).
\(n=800, p_{i}=0.7\)Find the expected frequency for the values of \(n\) and \(p_{i}\).
\(n=350, p_{i}=0.35\)Find the expected frequency for the values of \(n\) and \(p_{i}\).
\(n=610, p_{i}=0.89\)Find the expected frequency for the values of \(n\) and \(p_{i}\).
A researcher claims that the number of violent crimes in England and Wales by year is uniformly distributed. To test this claim, you randomly select 22,526 crimes from recent years and record the
An organization claims that the number of people visiting Egypt each year, which includes students, patients, and tourists, is not uniformly distributed. To test this claim, you randomly select 2000
Find the expected frequency for each cell in the contingency table. Assume that the variables favorite way to eat ice cream and gender are independent. Gender Cup Cone Favorite way to eat ice cream
The contingency table shows the results of a random sample of 2197 adults classified by their favorite way to eat ice cream and gender. The expected frequencies are displayed in parentheses. At
A health club manager wants to determine whether the number of days per week that college students exercise is related to gender. A random sample of 275 college students is selected and the results
Is the chi-square homogeneity of proportions test a left-tailed, right-tailed, or two-tailed test?Use this information about the homogeneity of proportions test. Another chi-square test that involves
Explain how the chi-square independence test is different from the chi-square homogeneity of proportions test.Use this information about the homogeneity of proportions test. Another chi-square test
In your opinion, how safe is the food you buy? CBS News polled 1048 U.S. adults and asked them the question below.Overall, how confident are you that the food you buy is safe to eat: very confident,
Find the critical \(F\)-value for a right-tailed test when \(\alpha=0.10\), d.f. \(_{\mathrm{N}}=5\), and d.f. \(_{\mathrm{D}}=28\).
Find the critical \(F\)-value for a two-tailed test when \(\alpha=0.05\), d.f. \(_{\mathrm{N}}=4\), and d.f. \(_{\mathrm{D}}=8\).
A restaurant manager is designing a system that is intended to decrease the variance of the time customers wait before their meals are served. Under the old system, a random sample of 10 customers
You want to purchase stock in a company and are deciding between two different stocks. Because a stock's risk can be associated with the standard deviation of its daily closing prices, you randomly
\(\alpha=0.05\), d.f. \({ }_{\mathrm{N}}=9\), d.f. \(_{\mathrm{D}}=16\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and
\(\alpha=0.01\), d.f. \(_{\mathrm{N}}=2\), d.f. \(_\mathrm{D}=11\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
\(\alpha=0.10\), d.f. \({ }_{\mathrm{N}}=10\), d.f. \(_{\mathrm{D}}=15\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and
\(\alpha=0.025\), d.f. \(_{\mathrm{N}}=7\), d.f. \(_{\mathrm{D}}=3\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
City A claims that the variance of its drunk-driving accidents is less than the variance of the drunk-driving accidents in City B. A sample of the drunk-driving cases of 15 of City A's accidents has
\(\alpha=0.05\), d.f. \(_{\mathrm{N}}=6\), d.f. \(_{\mathrm{D}}=3\)Find the right- and left-tailed critical F-values for a two-tailed test using the level of significance \(\alpha\) and degrees of
\(\alpha=0.10\), d.f. \(_{\mathrm{N}}=20\), d.f. \(_{\mathrm{D}}=15\)Find the right- and left-tailed critical F-values for a two-tailed test using the level of significance \(\alpha\) and degrees of
A medical researcher wants to determine whether there is a difference in the mean lengths of time it takes three types of pain relievers to provide relief from headache pain. Several headache
A researcher believes that for city driving, the fuel economy of compact, midsize, and large cars are the same. The gas mileages (in miles per gallon) for city driving for several randomly selected
The contingency table shows the results of a random sample of individuals by gender and type of vehicle owned. At \(\alpha=0.01\), can you conclude that gender is related to the type of vehicle
\(\alpha=0.05\), d.f. \(_{\mathrm{N}}=6\), d.f. \(_{\mathrm{D}}=50\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
\(\alpha=0.01\), d.f. \(_{\mathrm{N}}=12\), d.f. \(_{\mathrm{D}}=10\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and
\(\alpha=0.10\), d.f. \(_{\mathrm{N}}=5\), d.f. \(_{\mathrm{D}}=12\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
\(\alpha=0.05\), d.f. \(_{\mathrm{N}}=20\), d.f. \(_{\mathrm{D}}=25\)Find the critical F-value for a right-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and
\(\alpha=0.10\), d.f. \(_{\mathrm{N}}=15\), d.f. \(_{\mathrm{D}}=27\)Find the critical F-value for a two-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
\(\alpha=0.05\), d.f. \(_{\mathrm{N}}=9\), d.f. \(_{\mathrm{D}}=8\)Find the critical F-value for a two-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
\(\alpha=0.01\), d.f. \(_{\mathrm{N}}=40\), d.f. \(_{\mathrm{D}}=60\)Find the critical F-value for a two-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
\(\alpha=0.01\), d.f. \(_{\mathrm{N}}=11\), d.f. \(_{\mathrm{D}}=13\)Find the critical F-value for a two-tailed test using the level of significance \(\alpha\) and degrees of freedom d.f.N and d.f.D.
An instructor claims that the variance of SAT critical reading scores for females is different than the variance of SAT critical reading scores for males. The table shows the SAT critical reading
Does the distribution for people in the United States ages 25 and older differ from the distribution for people in the United States ages 30-34? Use \(\alpha=0.05\).(a) identify the claim and state
Use the data for 30 - to 34 -year-olds and 65 - to 69 -year-olds to test whether age and educational attainment are related. Use \(\alpha=0.01\).(a) identify the claim and state \(H_{0}\) and
At \(\alpha=0.01\), is there enough evidence to conclude that the variances of the annual wages for Ithaca, NY, and Little Rock, AR, are different?(a) identify the claim and state \(H_{0}\) and
Are the mean annual wages the same for all three cities? Use \(\alpha=0.10\). Assume that the population variances are equal.(a) identify the claim and state \(H_{0}\) and \(H_{a}\),(b) find the
In a survey of 3015 U.S. adults, \(80 \%\) say their household contains a desktop or laptop computer.(a) Construct a 95\% confidence interval for the proportion of U.S. adults who say their household
The table shows the gas mileages (in miles per gallon) of eight cars with and without using a fuel additive. At \(\alpha=0.10\), is there enough evidence to conclude that the additive improved gas
\(c=0.95, \bar{x}=26.97, \sigma=3.4, n=42\)Construct the indicated confidence interval for the population mean \(\mu\). Which distribution did you use to create the confidence interval?
\(c=0.95, \bar{x}=3.46, s=1.63, n=16\)Construct the indicated confidence interval for the population mean \(\mu\). Which distribution did you use to create the confidence interval?
\(c=0.99, \bar{x}=12.1, s=2.64, n=26\)Construct the indicated confidence interval for the population mean \(\mu\). Which distribution did you use to create the confidence interval?
\(c=0.90, \bar{x}=8.21, \sigma=0.62, n=8\)Construct the indicated confidence interval for the population mean \(\mu\). Which distribution did you use to create the confidence interval?
\(\mu
\(p \geq 0.19\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(\sigma=0.63\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(\mu eq 2.28\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
A pediatrician claims that the mean birth weight of a single-birth baby is greater than the mean birth weight of a baby that has a twin. The mean birth weight of a random sample of 85 single-birth
The mean room rate for two adults for a random sample of 26 three-star hotels in Cincinnati has a sample standard deviation of \(\$ 31\). Assume the population is normally distributed.(a) Construct a
An education organization claims that the mean SAT scores for male athletes and male non-athletes at a college are different. A random sample of 26 male athletes at the college has a mean SAT score
The annual earnings (in dollars) for 30 randomly selected locksmiths are shown below. Assume the population is normally distributed.(a) Construct a \(95 \%\) confidence interval for the population
A medical research team studied the use of a marijuana extract to treat children with an epilepsy disorder. Of the 52 children who were given the extract, the number of convulsive seizures was
A random sample of 40 ostrich eggs has a mean incubation period of 42 days. Assume the population standard deviation is 1.6 days.(a) Construct a 95\% confidence interval for the population mean
A researcher claims that \(5 \%\) of people who wear eyeglasses purchase their eyeglasses online. Describe type I and type II errors for a hypothesis test of the claim.
An economist wants to determine whether there is a linear relationship between a country's gross domestic product (GDP) and carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) emissions. The data are
A student conducts a study to determine whether there is a linear relationship between the number of hours a student exercises each week and the student's grade point average (GPA). The data are
Old Faithful, located in Yellowstone National Park, is the world's most famous geyser. The durations (in minutes) of several of Old Faithful's eruptions and the times (in minutes) until the next
Calculate the correlation coefficient for the gross domestic products and carbon dioxide emissions data in Example 1. Interpret the result in the context of the data.Data from Example 1An economist
Use technology to calculate the correlation coefficient for the Old Faithful data in Example 3. Interpret the result in the context of the data.Data from Example 3Old Faithful, located in Yellowstone
In Example 5, you used 25 pairs of data to find \(r \approx 0.979\). Is the correlation coefficient significant? Use \(\alpha=0.05\).Data from Example 5Use technology to calculate the correlation
In Example 4, you used 10 pairs of data to find \(r \approx 0.874\). Test the significance of this correlation coefficient. Use \(\alpha=0.05\).Data from Example 4Calculate the correlation
The weight (in kilograms) of 8 males and the circumference of their waists (in centimeters)(a) display the data in a scatter plot,(b) calculate the sample correlation coefficient \(r\),(c) describe
In Exercise 24, add data for a male with a weight of 105.6 kilograms and a waist size of 98.3 centimeters to the data set. Describe how this affects the correlation coefficient \(r\).Data from
In Exercise 25, add data for an international soccer player with a maximum weight of 180 kilograms and a jump height of 50 centimeters to the data set. Describe how this affects the correlation
In Exercise 26, remove the data for the international soccer player who can perform the half squat with a maximum of 210 kilograms and can sprint 10 meters in 1.42 seconds from the data set. Describe
Find the equation of the regression line for the gross domestic products and carbon dioxide emissions data used. GDP (in trillions of dollars), .x 1.8 CO2 emissions (in millions of metric tons), y
Use technology to find the equation of the regression line for the Old Faithful data used. Duration, Time, Duration, Time, x y x y 1.80. 56 3.78 79 1.82 58 3.83 85 1.90 62 3.88 80 1.93 56 4.10 89
The regression equation for the gross domestic products (in trillions of dollars) and carbon dioxide emissions (in millions of metric tons) data isUse this equation to predict the expected carbon
The number of athletes participating and the number of medals won in the Olympics by Japan through the last nine years (a) \(x=75\) athletes(b) \(x=80\) athletes(c) \(x=85\) athletes(d) \(x=120\)
The square meters and sale prices (in thousands of Egyptian Pounds) of seven offices in Egypt are shown in the table at the left.(a) \(x=45\) square meters(b) \(x=55\) square meters(c) \(x=95\)
The number of hours 9 students spent studying for a test and their scores on that test(a) \(x=3.5\) hours(b) \(x=5\) hours(c) \(x=7.5\) hours(d) \(x=14\) hoursFind the equation of the regression
The caloric contents and the sodium contents (in milligrams) of 12 brands of beef hot dogs.(a) \(x=170\) calories(b) \(x=100\) calories(c) \(x=260\) calories(d) \(x=210\) caloriesFind the equation of
The correlation coefficient for the gross domestic products and carbon dioxide emissions data is r ≈ 0.874.Find the coefficient of determination. What does this tell you about the explained
The regression equation for the gross domestic products and carbon dioxide emissions data isFind the standard error of estimate. = 199.535x + 56.036.
Using the results of Example 2, construct a \(90 \%\) prediction interval for the carbon dioxide emissions when the gross domestic product is \(\$ 2.8\) trillion. What can you conclude?Data from
The coefficient of determination \(r^{2}\) is the ratio of which two types of variations? What does \(r^{2}\) measure? What does \(1-r^{2}\) measure?
The Australian voting age populations (in millions) and the number of votes cast (in millions) for the democratic elections for nine election years are shown in the table. The equation of the
The table shows the quantity of wheat (in millions of kilograms per year) produced by India and the quantity of wheat (in millions of kilograms per year) exported by India for seven years. The
Construct a \(99 \%\) prediction interval for number of votes cast in Exercise 16 when the voting age population is 15 million.Data from Exercises 16The Australian voting age populations (in
Wheat Construct an \(80 \%\) prediction interval for the quantity of wheat exported by India in Exercise 17 when the quantity of wheat produced by India is 99,000 million kilograms per year.Data from
A researcher wants to determine how employee salaries at a company are related to the length of employment, previous experience, and education. The researcher selects eight employees from the company
Use the regression equation\[ \hat{y}=49,764+364 x_{1}+228 x_{2}+267 x_{3} \]found in Example 1 to predict an employee's salary for each set of conditions.1. 12 years of current employment 5 years
The mean score on a reading assessment test for 49 randomly selected male high school students was 279. Assume the population standard deviation is 41. The mean score on the same test for 50 randomly
A music teacher claims that the mean scores on a music assessment test for eighth grade boys and girls are equal. The mean score for 13 randomly selected boys is 142 with a standard deviation of 49 ,
The table shows the credit scores for 12 randomly selected adults who are considered high-risk borrowers before and two years after they attend a personal finance seminar. At \(\alpha=0.01\), is
In a random sample of 1020 U.S. adults in a recent year, 459 approve of the job the Supreme Court is doing. In another random sample of 1510 U.S. adults taken 3 years prior, 694 approve of the job
Claim: \(\mu_{1} \leq \mu_{2} ; \alpha=0.10\). Assume \(\sigma_{1}^{2} eq \sigma_{2}^{2}\)Sample statistics: \(\bar{x}_{1}=664.5, s_{1}=2.4, n_{1}=40\) and\[ \bar{x}_{2}=665.5, s_{2}=4.1, n_{2}=40
Claim: \(\mu_{1} \geq \mu_{2} ; \alpha=0.01\). Assume \(\sigma_{1}^{2}=\sigma_{2}^{2}\)Sample statistics: \(\bar{x}_{1}=44.5, s_{1}=5.85, n_{1}=17\) and\[ \bar{x}_{2}=49.1, s_{2}=5.25, n_{2}=18
Claim: \(\mu_{1}>\mu_{2} ; \alpha=0.10\). Assume \(\sigma_{1}^{2} eq \sigma_{2}^{2}\)Sample statistics: \(\bar{x}_{1}=520, s_{1}=25, n_{1}=7\) and\[ \bar{x}_{2}=500, s_{2}=55, n_{2}=6 \]Test the
A study of 200 randomly selected occupants in passenger cars and 250 randomly selected occupants in pickup trucks shows that \(91.0 \%\) of occupants in passenger cars and \(83.2 \%\) of occupants in
A medical research team conducted a study to test the effect of a cholesterolreducing medication. At the end of the study, the researchers found that of the 4700 randomly selected subjects who took
Hypothesis testing enables you to determine whether differences in samples indicate actual differences in populations or are merely due to sampling error. For instance, a study conducted on about
Find the critical value x20 for a right-tailed test when n = 26 and α = 0.10.
Find the critical value x20 for a left-tailed test when n = 11 and α = 0.01.
Find the critical values x2L and x2R for a two-tailed test when n = 9 and α = 0.05.
A dairy processing company claims that the variance of the amount of fat in the whole milk processed by the company is no more than 0.25. You suspect this is wrong and find that a random sample of 41
A company claims that the standard deviation of the lengths of time it takes an incoming telephone call to be transferred to the correct office is less than 1.4 minutes. A random sample of 25

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