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statistics
elementary statistics in social research
Elementary Statistics Picturing The World 7th Global Edition Betsy Farber, Ron Larson - Solutions
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 wants to determine whether there is a linear relationship between a country's gross domestic product
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 National Park, is the world's most famous geyser. The durations (in minutes) of several of Old
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 coefficient for the Old Faithful data in Example 3. Interpret the result in the context of the
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 coefficient for the gross domestic products and carbon dioxide emissions data in Example 1. Interpret the
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 the type of correlation, if any, and interpret the correlation in the context of the data, and(d) use
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 Exercises 24The weight (in kilograms) of 8 males and the circumference of their waists (in centimeters)
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 coefficient \(r\).Data from Exercises 25The maximum weights (in kilograms) for which one repetition of a
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 how this affects the correlation coefficient \(r\).Data from Exercises 26The maximum weights (in
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 604.4 1.3 434.2 2.4 544.0 1.5 370.4 3.9 742.3 2.1 340.5 0.9 232.0 1.4 262.3 3.0 441.9 4.6 1157.7
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 1.98 57 4.27 90 2.05 57 4.30 89 2.13 60 4.43 89 2.30 57 4.47 86 2.37 61 4.53 89 2.82 73 4.55 86 3.13 76
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 dioxide emissions for each gross domestic product.1. \(\$ 1.2\) trillion 2. \(\$ 2.0\) trillion 3.
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) \(x=120\) athletesFind the equation of the regression line for the data. Then construct a scatter plot of the
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) \(x=95\) square meters(d) \(x=125\) square metersFind the equation of the regression line for the data. Then
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 line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair
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 regression line for the data. Then construct a scatter plot of the data and draw the regression
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 variation of the data about the regression line? about the unexplained variation?
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 Example 2The regression equation for the gross domestic products and carbon dioxide emissions data is
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 regression line is \(\hat{y}=0.8194 x+1.842\).Use the data to(a) find the coefficient of determination
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 equation of the regression line is \(\hat{y}=0.249 x-19023\).Use the data to(a) find the coefficient of
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 millions) and the number of votes cast (in millions) for the democratic elections for nine election years
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 Exercises 17The table shows the quantity of wheat (in millions of kilograms per year) produced by
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 and obtains the data shown in the table.Use Minitab to find a multiple regression equation that
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 of previous experience 16 years of education 2. 4 years of current employment 2 years of previous
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 selected female high school students was 278.Assume the population standard deviation is 39 . At
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 , and the mean score for 15 randomly selected girls is 156 with a standard deviation of 42 . At
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 there enough evidence to support the claim that the personal finance seminar helps adults increase their
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 the Supreme Court is doing. At \(\alpha=0.05\), can you support the claim that the proportion of U.S.
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\[ \bar{x}_{2}=665.5, s_{2}=4.1, n_{2}=40 \]Test the claim about the difference between two population means \(\mu_{1}\) and \(\mu_{2}\) at
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\[ \bar{x}_{2}=49.1, s_{2}=5.25, n_{2}=18 \]Test the claim about the difference between two population means \(\mu_{1}\) and \(\mu_{2}\) at the
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 claim about the difference between two population means \(\mu_{1}\) and \(\mu_{2}\) at the level of
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 pickup trucks wear seat belts. At \(\alpha=0.10\), can you reject the claim that the proportion of
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 the medication, 301 died of heart disease. Of the 4300 randomly selected subjects who took a placebo,
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 1400 American children in a variety of settings compared the behavior of the children who attended day
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 milk containers has a variance of 0.27. At α = 0.05, is there enough evidence to reject the
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 incoming telephone calls has a standard deviation of 1.1 minutes. At α = 0.10, is there enough evidence to
A sporting goods manufacturer claims that the variance of the strengths of a certain fishing line is 15.9. A random sample of 15 fishing line spools has a variance of 21.8. At α = 0.05, is there enough evidence to reject the manufacturer’s claim? Assume the population is normally distributed.
Claim: σ2 ≤ 17.6; α = 0.01. Sample statistics: s2 = 28.33, n = 41 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population is normally distributed.
Claim: σ2 > 19; α = 0.1. Sample statistics: s2 = 28, n = 17 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population is normally distributed.
Claim: σ2 ≠ 32.8; α = 0.1. Sample statistics: s2 = 40.9, n = 101 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population is normally distributed.
Claim: σ2 = 63; α = 0.01. Sample statistics: s2 = 58, n = 29 Test the claim about the population variance σ2 or standard deviation σ at the level of significance α. Assume the population is normally distributed.
A helmet manufacturer claims that the variance of the thickness in a helmet model is 7.5. A random sample of 15 helmets has a variance of 2.7. At α = 0.10, is there enough evidence to reject the claim?(a) identify the claim and state H0 and Ha,(b) find the critical value(s) and identify the
A library claims that the standard deviation of the reading days for readers of a particular book is no more than 2 days. A random sample of 30 readers has a standard deviation of 3 days. At α = 0.10, is there enough evidence to reject the claim?(a) identify the claim and state H0 and Ha,(b) find
\(\mu \leq 100\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(\mu eq 48\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(p
\(\mu=16\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(\sigma>2.5\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
\(p \leq 0.4\)The statement represents a claim. Write its complement and state which is \(H_{0}\) and which is \(H_{a}\).
A car rental company claims that its cars are driven for at least 10,000 miles on an average.(a) state the null and alternative hypotheses and identify which represents the claim, (b) describe type I and type II errors for a hypothesis test of the claim, (c) explain whether the hypothesis test is
A soft drink manufacturing company claims that the mean number of milligrams of sodium in one serving is less than 25.(a) state the null and alternative hypotheses and identify which represents the claim, (b) describe type I and type II errors for a hypothesis test of the claim, (c) explain whether
Left-tailed test, \(z=-1.18, \alpha=0.05\)Find the P-value for the hypothesis test with the standardized test statistic \(z\). Decide whether to reject \(H_{0}\) for the level of significance \(\alpha\).
Two-tailed test, \(z=2.57, \alpha=0.10\)Find the P-value for the hypothesis test with the standardized test statistic \(z\). Decide whether to reject \(H_{0}\) for the level of significance \(\alpha\).
Claim: \(\mathrm{H}_{0}: \mu=3725 ; \alpha=0.10 ; \sigma=121\). Sample statistics: \(\bar{x}=3748, n=30\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population is normally distributed.
Claim: \(\mu
Claim: \(\mu eq 21.25 ; \alpha=0.03 ; \sigma=4.35\). Sample statistics: \(\bar{x}=19.7, n=60\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population is normally distributed.
Claim: \(\mu=930 ; \alpha=0.10 ; \sigma=30\). Sample statistics: \(\bar{x}=937, n=30\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population is normally distributed.
Two-tailed test, \(\alpha=0.05, n=18\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Left-tailed test, \(\alpha=0.025, n=39\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Right-tailed test, \(\alpha=0.05, n=12\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Two-tailed test, \(\alpha=0.01, n=20\)Find the critical value(s) and rejection region(s) for the type of \(t\)-test with level of significance \(\alpha\) and sample size \(n\).
Claim: \(\mu
Claim: \(\mu=195 ; \alpha=0.10\). Sample statistics: \(\bar{x}=190, s=36, n=101\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population is normally distributed.
Claim: \(\mu eq 3,330,000 ; \alpha=0.05\). Sample statistics: \(\bar{x}=3,293,995, s=12,801, n=35\)Test the claim about the population mean \(\mu\) at the level of significance \(\alpha\). Assume the population is normally distributed.
Claim: \(p
Right-tailed test, \(n=20, \alpha=0.05\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
Two-tailed test, \(n=14, \alpha=0.01\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
Two-tailed test, \(n=41, \alpha=0.10\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
Left-tailed test, \(n=6, \alpha=0.05\)Find the critical value(s) and rejection region(s) for the type of chi-square test with sample size \(n\) and level of significance \(\alpha\).
A hat company claims that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15. At α = 0.01, can you reject the company’s claim? Assume the population is normally distributed and the population standard deviation is 0.27.(a) Identify the claim and
A travel analyst claims the mean daily base price for renting a full-size or less expensive vehicle in Vancouver, Washington, is more than \($36.\) You want to test this claim. In a random sample of 40 full-size or less expensive vehicles available to rent in Vancouver, Washington, the mean daily
A government agency reports that the mean amount of earnings for full-time workers ages 18 to 24 with a bachelor’s degree in a recent year is $47,254.In a random sample of 15 full-time workers ages 18 to 24 with a bachelor’s degree, the mean amount of earnings is $50,781 and the standard
A weight loss program claims that program participants have a mean weight loss of at least 10.5 pounds after 1 month. The weight losses after 1 month (in pounds) of a random sample of 40 program participants are listed below. At α = 0.01, is there enough evidence to reject the program’s
A nonprofit consumer organization says that less than 18% of the vehicles the organization rated in a recent year have an overall score of 78 or more.In a random sample of 90 vehicles the organization rated in a recent year, 20% have an overall score of 78 or more. At α = 0.05, can you support the
In Exercise 5, the nonprofit consumer organization says that the standard deviation of the vehicle rating scores is 11.90. A random sample of 90 vehicle rating scores has a standard deviation of 11.96. At α = 0.10, is there enough evidence to reject the organization’s claim? Assume the
Classify each pair of samples as independent or dependent.1. Sample 1: Triglyceride levels of 70 patients Sample 2: Triglyceride levels of the same 70 patients after using a triglyceride-lowering drug for 6 months.2. Sample 1: Scores for 38 adult males on a psychological screening test for
A credit card watchdog group claims that there is a difference in the mean credit card debts of people in California and Florida. The results of a random survey of 250 people from each state are shown at the left. The two samples are independent. Assume that σ1 = $960 for California and σ2 = $845
A travel agency claims that the average daily cost of meals and lodging for vacationing in Texas is less than the average daily cost in Virginia. The table at the left shows the results of a random survey of vacationers in each state. The two samples are independent. Assume that σ1 = $20 for Texas
A non-governmental organization wants to choose between two regions in a state to initiate a campaign for rainwater harvesting. A researcher claims that Region A receives lesser rainfall than Region B. To test the regions, the average rainfall is calculated for 60 days in each region. The mean
The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown at the left. Can you conclude that there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.10. Assume the
A channel claims that the mean amount of money spent by a family at movie theaters is greater than the mean amount spent by a family at amusement parks. The results for samples of expenses for the two modes of entertainment are shown at the left. At \(\alpha=0.01\), can you support the channel's
A manager claims that the defects in units produced at Site A are more than the defects in units produced at Site B. The sample of 23 units from Site A contain a mean of 78 defects and a standard deviation of 6 defects. The sample of 19 units from Site B contain a mean of 75 defects and a standard
In a study published in the Journal of the American Medical Association, three groups of 18 - to 35 -year-old participants overate for an 8 -week period. The groups consumed different levels of protein in their diet. The low protein group's diet was \(5 \%\) protein, the normal protein group's diet
A shoe manufacturer claims that athletes can increase their vertical jump heights using the manufacturer's training shoes. The vertical jump heights of eight randomly selected athletes are measured. After the athletes have used the shoes for 8 months, their vertical jump heights are measured again.
The campaign staff for a state legislator wants to determine whether the legislator's performance rating \((0-100)\) has changed from last year to this year. The table below shows the legislator's performance ratings from the same 16 randomly selected voters for last year and this year. At
A cookie manufacturer claims that its new cookies have more fiber than the ones produced by its competitor. The table shows the fiber content in seven samples of each type of cookies produced by the manufacturer and his competitor. At \(\alpha=0.01\), is there enough evidence to support the cookie
In a derby, eight jockeys are riding a few exceptionally well-trained horses. As part of the race, the horses are timed as they run an obstacle course. The table shows the times (in seconds) of the horses in the first lap and the final lap of the race. At \(\alpha=0.05\), is there enough evidence
The standard deviation of the sale price of a bike is no more than $225.Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
A museum claims that its mean daily attendance is at least 300 people.Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
A microwave manufacturer claims that the mean life of the thermostat for a certain model of microwave is more than 4 years.Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
As stated by a courier company’s dispatch department, the number of delivery errors per million consignments has a standard deviation that is less than 2.Write the claim as a mathematical statement. State the null and alternative hypotheses, and identify which represents the claim.
An online food delivery website claims that at least 75% of its new customers will return to place their next order.Describe type I and type II errors for a hypothesis test of the indicated claim.
A hose manufacturer claims that the maximum water flow rate in a garden is 40 liters per minute.Describe type I and type II errors for a hypothesis test of the indicated claim.
A local cricket club claims that the length of time to bowl an over has a standard deviation of more than 4 minutes.Describe type I and type II errors for a hypothesis test of the indicated claim.
A researcher claims that the percentage of adults in Egypt who own a surround sound speaker is not 40%.Describe type I and type II errors for a hypothesis test of the indicated claim.
A data encryption company publicizes that at least 98% of the systems using their software are protected.Describe type I and type II errors for a hypothesis test of the indicated claim.
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