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statistics

Elementary Statistics 12th Edition Mario F. Triola - Solutions

What percentage of the total variation in height can be explained by the linear correlation between foot length and height?Refer to the Minitab display obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of the 40 people listed in Data Set 2 of Appendix B. Along with
For someone with a foot length of 29.0 cm, identify the 95% prediction interval estimate of their height, and write a statement interpreting that interval.Refer to the Minitab display obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of the 40 people listed in Data
Foot length: 25.0 cm; 95% confidence. Use the paired data consisting of foot lengths (cm) and heights (cm) of the 40 people listed in Data Set 2 of Appendix B. Let x represent foot length and let y represent the corresponding height. Use the given foot length and the given confidence level to
Foot length: 25.0 cm; 99% confidence. Use the paired data consisting of foot lengths (cm) and heights (cm) of the 40 people listed in Data Set 2 of Appendix B. Let x represent foot length and let y represent the corresponding height. Use the given foot length and the given confidence level to
Foot length: 22.0 cm; 90% confidence. Use the paired data consisting of foot lengths (cm) and heights (cm) of the 40 people listed in Data Set 2 of Appendix B. Let x represent foot length and lety represent the corresponding height. Use the given foot length and the given confidence level to
Foot length: 26.0 cm; 95% confidence. Use the paired data consisting of foot lengths (cm) and heights (cm) of the 40 people listed in Data Set 2 of Appendix B. Let x represent foot length and let y represent the corresponding height. Use the given foot length and the given confidence level to
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).Find the(a) Explained
Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars, and all of the towns are in Dutchess County, New York. For the prediction interval, use a 99% confidence level with a court income of $800,000.Find the(a) Explained
The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected clusters of galaxies. For the prediction interval, use a 90% confidence level with a redshift of the cluster Fiydra of 0.0126.Find the(a) Explained variation,(b) Unexplained
The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. For the prediction interval, use a 95% confidence level with a diamond that weighs 0.8 carats.Find the(a) Explained variation,(b) Unexplained variation, and(c) Indicated prediction interval. In each case,
Confidence intervals for the y-intercept Î²0 and slope Î²1 for a regression line (y = Î²0 + Î²1x) can be found by evaluating the limits in the intervals below.b0 EWhere b1 - EThe y-intercept b0 and the slope b1 are found from the sample data and tÎ±/2 is found from Table A-3 by using n
Example 1 in this section illustrated the procedure for finding a prediction interval for an individual value of y. When using a specific value x0 for predicting the mean of all values of y, the confidence interval is as follows:WhereThe critical value tÎ±/2 is found with n €” 2 degrees of
For the regression equation given in Exercise 1, the P-value is 0.000 and the adjusted R2 value is 0.925. If we were to include an additional predictor variable of neck size (in.), the P-value becomes 0.000 and the adjusted R2 becomes 0.933. Given that the adjusted R2 value of 0.933 is larger, is
For Exercise 2, why is it better to use values of adjusted R2 instead of simply using values of R2?
For the multiple regression equation given in Exercise 1, we get R2 = 0.928. What does that value tell us?
We want to consider the correlation between LDL cholesterol and the predictor variables of weight (W7) and systolic blood pressure (SYS) for females. Refer to the Minitab display and answer the given questions or identify the indicated items. The Minitab display is based on the measured values of
Should the multiple regression equation be used for predicting the LDL cholesterol level based on weight and diastolic blood pressure? Why or why not?We want to consider the correlation between LDL cholesterol and the predictor variables of weight (W7) and systolic blood pressure (SYS) for females.
A female weighs 59.3 kg and she has a measured systolic blood pressure of 122 mm Hg. Use the multiple regression equation to determine the predicted LDL cholesterol amount. Is the result likely to be a good predicted value? Why or why not?We want to consider the correlation between LDL cholesterol
If only one predictor (x) variable is used to predict the city fuel consumption, which single variable is best? Why?Refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 14 in Appendix B. The response (y) variable is CITY (fuel consumption in mils-al).
If exactly two predictor (x) variables are to be used to predict the city fuel consumption, which two variables should be chosen? Why?Refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 14 in Appendix B. The response (y) variable is CITY (fuel
Which regression equation is best for predicting city fuel consumption? Why?Refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 14 in Appendix B. The response (y) variable is CITY (fuel consumption in mils-al). The predictor (x) variables are WT
A Honda Civic weighs 2740 lb, it has an engine displacement of 1.8 L, and its highway fuel consumption is 36 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?Refer to the
Refer to Data Set 10 in Appendix B and use the tar, nicotine, and CO amounts for the cigarettes that are 100 mm long, filtered, nonmenthol, and nonlight (the last set of measurements). Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it best? Is the
Repeat the preceding exercise using the sample data from the Menthol cigarettes listed in Data Set 10 from Appendix B.
Refer to Data Set 6 in Appendix B and find the best regression equation with IQ score as the response (y) variable. Use predictor variables of brain volume and/or body weight. Why is this equation best? Based on these results, can we predict someone’s IQ score if we know their brain volume and
Refer to Data Set 5 in Appendix B and find the best regression equation with IQF (full IQ score) as the response (y) variable. Use predictor variables of IQV (verbal IQ score) and IQP (performance IQ score). Why is this equation best? Based on these results, can we predict someone’s full IQ score
If the coefficient Î²1 has a non-zero value, then it is helpful in predicting the value of the response variable. If Î²1 = 0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that
A confidence interval for the regression coefficient Î²1, is expressed as Î²1 €” E
Refer to Data Set 7 in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response (y) variable represent weight, use the variable of age and the dummy variable of sex to find the multiple regression equation. Use the
Let x represent years coded as 1, 2, 3, . . . for years starting in 1980, and lety represent the numbers of points scored in each Super Bowl from 1980. Using the data from 1980 to the last Super Bowl at the time of this writing, we obtain the following values of R2 for the different models: linear:
In Exercise 2, the quadratic model results in R2 = 0.103. Identify the percentage of the variation in Super Bowl points that can be explained by the quadratic model relating the variable of year and the variable of points scored. What does the result suggest about the usefulness of the quadratic
The accompanying graph plots the numbers of points scored in each Super Bowl from 1980 (coded as year 1) to the last Super Bowl at the time of this writing. The graph also shows the graph of the quadratic equation that best fits the data. What feature of the graph justifies the value of R2 = 0.103
The table lists the distance d (meters) above the ground for an object dropped in a vacuum from a height of 300 m. The time t (in sec) is the time after the object has been released.Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is
The table lists the cost y (in dollars) of purchasing a volume of red landscaping mulch from the Red Barn Farm and Nursery in Dutchess County, New York. The mulch is sold by the €œyard,€ which is actually a cubic yard, and the variable x is the length (yd) of each side of a cubic
The table lists the value y (in dollars) of $100 deposited in a certificate of deposit at Bank of New York.Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear,
The table lists intensities of sounds as multiples of a basic reference sound. A scale similar to the decibel scale is used to measure the sound intensity.Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the
Listed below are the amounts (millions of dollars) grossed during the first three weeks of the movie Harry Potter and the Half Blood Prince. Use the best model to predict the gross amount on the 22nd day of the movie€™s release. Is the result close to the actual amount of $2.2 million? Is there
Listed below are the numbers of deaths in the United States resulting from motor vehicle crashes. Use the best model to find the projected number of such deaths for the year 2020.Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to
The table lists different amounts (metric tons) of the explosive TNT and the corresponding value on the Richter scale used for explosions of the TNT.Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of
According to Benford€™s law, a variety of different data sets include numbers with leading (first) digits that occur with the proportions listed in the following table.Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used
In a carefully controlled experiment, bacteria are allowed to grow for a week. The number of bacteria are recorded at the end of each day with these results: 20, 40, 80, 160, 320, 640, 1280. Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the
Listed below in order by row are annual sunspot numbers beginning with 1980. Is the best model a good model? Carefully examine the scatterplot and identify the pattern of the points. Which of the models fits that pattern?Construct a scatterplot and identify the mathematical model that best fits the
Listed below in order by row are the annual high values of the Dow Jones Industrial Average for each year beginning with 1990. Use only the first 10 values (for 1990€” 1999) to find the best model and then predict the value for the year 2010. Is the predicted value close to the actual value of
Repeat the preceding exercise using all of the data values.Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power
In 1965, Intel cofounder Gordon Moore initiated what has since become known as Moore€™s law: the number of transistors per square inch on integrated circuits will double approximately every 18 months. In the table below, the first row lists different years and the second row lists the number of
In addition to the value of R2, another measurement used to assess the quality of a model is the sum of squares of the residuals. Recall from Section 10-3 that a residual is the difference between an observed y value and the value of y predicted from the model, which is denoted as y-hat. Better
The table below lists measurements from eight different eruptions of the Old Faithful geyser in Yellowstone National Park. The data consist of the duration (sec) of the eruption, height (ft) of the eruption, time interval (min) before the eruption, and time interval (min) after the eruption. Shown
Refer to the table of data given in Exercise 1 and use the heights and interval after times.a. Construct a scatterplot. What does the scatterplot suggest about a linear correlation between heights of eruptions and interval-after times? b. Find the value of the linear correlation coefficient and
Refer to the table of data given in Exercise 1 and use the durations and heights.a. Construct a scatterplot. What does the scatterplot suggest about a linear correlation between duration and height? b. Find the value of the linear correlation coefficient and determine whether there is sufficient
In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the height(m) of the soccer ball. What do you conclude about the relationship between time and height? What horrible
Refer to the sample data given in Exercise 1 and find the multiple regression equation with the response (y) variable of €œinterval-after€ time and predictor (x) variables of duration and €œinterval-before€ time. Identify the value of the multiple
Using only the weights before the diet, identify the highest weight and convert it to a z score. In the context of these sample data, is that highest value an €œunusual€ weight? Why or why not?
Test Use a 0.05 significance level to test the claim that the diet is effective.
Construct a 95% confidence interval estimate of the mean weight of subjects before the diet. Write a brief statement interpreting the confidence interval.
Use the before/after weights listed below.a. Test for a correlation between the before and after weights.b. If each subject were to weigh exactly the same after the diet as before, what would be the value of the linear correlation coefficient?c. If all subjects were to lose 5% of their weight from
Birth weights in the United States are normally distributed with a mean of 3420 g and a standard deviation of 495 g. a. What percentage of babies is born with a weight greater than 3500 g? b. Find P10, which is the 10th percentile. c. The Rockland Medical Center requires special treatment for
In a USA Today survey of 456 subjects, 269 answered “yes” to this question: “Is honesty always the best policy?” a. Use a 0.05 significance level to test the claim that the majority of us say that honesty is always the best policy. b. The survey results were obtained from Internet users who
The members of Congress have these religious affiliations: Catholic (156), Jewish (39), Protestant (304), Mormon (15), other (15). There were six members of Congress who did not specify a religious affiliation, and the data are current at the time of this writing. a. What is the level of
The members of Congress have these religious affiliations: Catholic (156), Jewish (39), Protestant (304), Mormon (15), other (15). There were six members of Congress who did not specify a religious affiliation, and the data are current at the time of this writing. a. If two different members of
Construct the graph that is most effective in depicting the religious affiliations of members of Congress. The members of Congress have these religious affiliations: Catholic (156), Jewish (39), Protestant (304), Mormon (15), other (15). There were six members of Congress who did not specify a
Exercise 1 includes results from a survey of 1005 randomly selected subjects. Consider the claim that when respondents select days of the week, the seven different days have the same chance of being selected. If that claim is true for the 1005 respondents, what is the expected value for each of the
The accompanying STATDISK display shows results from the claim and data given. Test that claim.Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion.
Example 1 in this section involved an analysis of the last digits of weights from a random sample of 100 Californians. Using those same subjects, the last digits of their heights are listed in the table below. Use a 0.05 significance level to test the claim that the sample is from a population of
The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the
A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn€™t have a flat tire, would they be able to identify the same tire? The
For a recent year, the following are the numbers of homicides that occurred each month in New York City: 38, 30, 46, 40, 46, 49, 47, 50, 50, 42, 37, 37. Use a 0.05 significance level to test the claim that homicides in New York City are equally likely for each of the 12 months. Is there sufficient
In his book Outliers, author Malcolm Gladwell argues that more baseball players have birthdates in the months immediately following July 31, because that was the cutoff date for nonschool baseball leagues. Here is a sample of frequency counts of months of birthdates of American-born major league
The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 31, 42, 40, 28, 32. Use a 0.05 significance level to test the claim that the outcomes are not
Records of randomly selected births were obtained and categorized according to the day of the week that they occurred. Because babies are unfamiliar with our schedule of weekdays, a reasonable claim is that births occur on the different days with equal frequency. See the table that follows. Use a
The table below lists the frequency of wins for different post positions in the Kentucky Derby horse race (current as of this writing). A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. Use a 0.05 significance level to test the claim that the
The author recorded all digits selected in New York’s Win 4 Lottery for two drawings held each day in a recent year. The frequencies of the digits from 0 through 9 are 280, 303, 331, 289, 285, 294, 283, 274, 297, and 284. Use a 0.05 significance level to test the claim of lottery officials that
The police department in Madison, Connecticut released the following numbers of calls for the different days of the week during a recent February that had 28 days: Monday (114); Tuesday (152); Wednesday (160); Thursday (164); Friday (179); Saturday (196); Sunday (130). Use a 0.01 significance level
Repeat the preceding exercise using these observed frequencies for police calls received during the month of March: Monday (208); Tuesday (224); Wednesday (246); Thursday (173); Friday (210); Saturday (236); Sunday (154). What is a fundamental error with this analysis? Conduct the hypothesis test
The table below lists the numbers of games played in the baseball World Series as of this writing. That table also includes the expected proportions for the numbers of games in a World Series, assuming that in each series, both teams have about the same chance of winning. Use a 0.05 significance
The contestants on the TV show American Idol try to win a singing contest. At one point, the web site WhatNotToSing.com listed the actual numbers of eliminations for different orders of singing, and the expected number of eliminations was also listed. The results are in the table below. Use a 0.05
Candies Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% brown. Refer to Data Set 20 in Appendix B and use the sample data to test the claim that the color distribution is as claimed by
In analyzing hits by V-l buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. Use the values listed and a 0.05 significance level to test
When working for the Brooklyn district attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 15, 0, 76, 479, 183, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2,
Exercise 21 lists the observed frequencies of leading digits from amounts on checks from seven suspect companies. Here are the observed frequencies of the leading digits from the amounts on checks written by the author: 68, 40, 18, 19, 8, 20, 6, 9, 12. (Those observed frequencies correspond to the
Frequencies of leading digits from IRS tax files are 152, 89, 63, 48, 39, 40, 28, 25, and 27. Using a 0.05 significance level, test for goodness-of-fit with Benford€™s law. Does it appear that the tax entries are legitimate?
The author recorded the leading digits of the sizes of the files stored on his computer, and the leading digits have frequencies of 45, 32, 18, 12, 9, 3, 13, 9, and 9. Using a 0.05 significance level, test for goodness-of-fit with Benford€™s law.
Refer to Data Set 1 in Appendix B for the 40 heights of females.a. Enter the observed frequencies in the table above.b. Assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, use the methods of Chapter 6 to find the probability of a randomly
The accompanying table summarizes successes and failures when subjects used different methods when trying to stop smoking. The determination of smoking or not smoking was made five months after the treatment was begun, and the data are based on results from the Centers for Disease Control and
The table in Exercise 1 is called a contingency table or two-way table. Why is the term contingency used? Why is the terminology of two-way table used?
Is the hypothesis test in Exercise 1 right-tailed, left-tailed, or two-tailed? Explain your choice.
In a study of the €œdenomination effect€ described in the Chapter Problem, 150 women in China were given either a single 100 Yuan bill or a total of 100 Yuan in smaller bills. The value of 100 Yuan is about $15. The women were given the choice of spending the money on specific items or they
A randomized controlled trial was designed to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel syndrome. Results are given in the table below. The results are based on evaluations made one year after the treatment. Minitab results are given below the table.
The table below includes results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table indicates when
The U.S. Supreme Court considered a case involving the exam for firefighter lieutenant in the city of New Haven, Connecticut. Results from the exam are shown in the table below. Is there sufficient evidence to support the claim that results from the test should be thrown out because they are
Many people believe that criminals who plead guilty tend to get lighter sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sample data for San Francisco defendants in burglary cases. All of the subjects had prior prison sentences. Use a 0.05
Alert nurses at the Veteran€™s Affairs Medical Center in Northampton, Massachusetts, noticed an unusually high number of deaths at times when another nurse, Kristen Gilbert, was working. Those same nurses later noticed missing supplies of the drug epinephrine, which is a synthetic
The table below shows results since 2006 of challenged referee calls in the U.S. Open. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether the call is overturned.
A random sample of 760 subjects was obtained, and each was tested for left-hand writing. Results are in the table below. Use a 0.05 significance level to test the claim that left-handedness is independent of gender.
In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The table below summarizes results from 286 kicks during games among top teams. In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of
A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table. Test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are
In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained. Use a 0.05 significance level to test the claim that getting a cold is independent of the treatment group. What do the results suggest about the effectiveness of echinacea as a
A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the table below. Test the claim that injuries are independent of helmet color. Should
A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below. At the 0.01 significance level, test the claim that the cooperation of the subject (response or refusal) is independent of the age category. Does any particular age group
In his book Outliers, author Malcolm Gladwell argues that more American-born baseball players have birthdates in the months immediately following July 31 because that was the cutoff date for nonschool baseball leagues. The table below lists months of births for a sample of American-born baseball
Lipitor is the trade name of the drug atorvastatin, which is used to reduce cholesterol in patients. Adverse reactions have been studied in clinical trials, and the table below summarizes results for infections in patients from different treatment groups. Use a 0.01 significance level to test the

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