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mathematics
statistics

Questions and Answers of Statistics

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
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
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
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
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
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
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%
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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.
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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),
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
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
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
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
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
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
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
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,
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
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
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,
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);
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);
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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

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