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elementary statistics
Elementary Statistics 9th Edition Mario F. Triola - Solutions
Forecast and Actual Temperatures Refer to Data Set 10 in Appendix B and use all of the actual low temperatures and the low temperatures that were forecast one day earlier.a. Using a 0.05 significance level, test the claim that there is no difference between the actual low temperatures and the low
Effects of an Outlier and Units of Measurementa. When using the methods of this section, can an outlier have a dramatic effect on the hypothesis test and confidence interval?b. The examples in this section used temperatures measured in degrees Fahrenheit. If we convert all sample temperatures from
Confidence Intervals and One-Sided Tests The 95% confidence interval for a collection of paired sample data is 0.0 , md , 1.2. Based on this confidence interval, the traditional method of hypothesis testing leads to the conclusion that the claim of md . 0 is supported. What is the smallest possible
Using the Correct Procedurea. Consider the sample data given below to be matched pairs and use a 0.05 significance level to test the claim that md . 0.b. Consider the sample data given below to be two independent samples. Use a 0.05 significance level to test the claim that m1 . m2.c. Compare the
Testing Effects of Zinc A study of zinc-deficient mothers was conducted to determine effects of zinc supplementation during pregnancy. Sample data are listed in the margin (based on data from “The Effect of Zinc Supplementation on Pregnancy Outcome,” by Goldenberg et al., Journal of the
Rainfall on Weekends USA Today and other newspapers reported on a study that supposedly showed that it rains more on weekends. The study referred to areas on the East Coast near the ocean. Data Set 11 in Appendix B lists the rainfall amounts in Boston for one year. The 52 rainfall amounts for
Tobacco and Alcohol Use in Animated Children’s Movies Data Set 7 in Appendix B lists times (in seconds) that animated children’s movies show tobacco use and alcohol use. The 50 times of tobacco use have a mean of 57.4 sec and a standard deviation of 104.0 sec. The 50 times of alcohol use have a
Calcium and Blood Pressure Sample data were collected in a study of calcium supplements and their effects on blood pressure. A placebo group and a calcium group began the study with blood pressure measurements (based on data from “Blood Pressure and Metabolic Effects of Calcium Supplementation in
Effect of an Outlier The methods of this section have a fairly strict requirement that the two populations have normal distributions. The presence of an outlier is evidence against a normally distributed population. Repeat Exercise 6 after deleting the outlier of 504 lb in the sample of axial loads
Determining P-Values To test a claim about two population variances by using the P-value approach, first find the F test statistic, then refer to Table A-5 to determine how it compares to the critical values listed for a 5 0.025 and a 5 0.05. Referring to Exercise 5, what can be concluded about the
Warmer Surgical Patients Recover Better? An article published in USA Today stated that “in a study of 200 colorectal surgery patients, 104 were kept warm with blankets and intravenous fluids; 96 were kept cool. The results show: Only 6 of those warmed developed wound infections vs. 18 who were
Historical Data Set In 1908, “Student” (William Gosset) published the article “The Probable Error of a Mean” (Biometrika, Vol. 6, No. 1). He included the data listed below for two different types of straw seed (regular and kiln dried) that were used on adjacent plots of land. The listed
Brain Volume and Psychiatric Disorders A study used x-ray computed tomography(CT) to collect data on brain volumes for a group of patients with obsessive-compulsive disorders and a control group of healthy persons. Sample results (in mL) are given below for total brain volumes (based on data from
Variation of Brain Volumes Use the same sample data given in Exercise 3 with a 0.05 significance level to test the claim that the populations of total brain volumes for obsessive-compulsive patients and the control group have different amounts of variation.
Carbon Monoxide and Cigarettes Refer to the given data for the measured amounts of carbon monoxide (CO) from samples of filtered and nonfiltered king-size cigarettes. All measurements are in milligrams, and the data are from the Federal Trade Commission. Use a 0.05 significance level to test the
Zinc for Mothers A study of zinc-deficient mothers was conducted to determine whether zinc supplementation during pregnancy results in babies with increased weights at birth. Sample data are listed in the margin (based on data from “The Effect of Zinc Supplementation on Pregnancy Outcome,” by
People Helping People In a study of people who stop to help drivers with disabled cars, researchers hypothesized that more people would stop to help someone if they first saw another driver with a disabled car getting help. In one experiment, 2000 drivers first saw a woman being helped with a flat
Testing Effects of Physical Training A study was conducted to investigate some effects of physical training. Sample data are listed below, with all weights given in kilograms. (See “Effect of Endurance Training on Possible Determinants of VO2 During Heavy Exercise,” by Casaburi et al., Journal
Speeding Tickets for Men and Women The data in the accompanying table were obtained through a survey of randomly selected subjects (based on data from R. H.Bruskin Associates).a. If one of the survey subjects is randomly selected, find the probability of getting someone ticketed for speeding.b. If
Cell Phones and Crashes: Analyzing Newspaper Report In an article from the Associated Press, it was reported that researchers “randomly selected 100 New York motorists who had been in an accident and 100 who had not. Of those in accidents, 13.7 percent owned a cellular phone, while just 10.6
Clinical Tests of Viagra In clinical tests of adverse reactions to the drug Viagra, 4.0%of the 734 subjects in the treatment group experienced nasal congestion, but 2.1% of the 725 subjects in the placebo group experienced nasal congestion (based on data from Pfizer Pharmaceuticals).a. Construct a
Marathon Finishers Refer to the results for female marathon runners in Data Set 8 in Appendix B.a. Find the proportion of female runners who finished the New York City marathon, then test the claim that the proportion is less than 0.5.b. For the times of the female finishers, find the mean, median,
Guns and Murder Rate Using data collected from the FBI and the Bureau of Alcohol, Tobacco, and Firearms, the number of registered automatic weapons and the murder rate (in murders per 100,000 people) was obtained for each of eight randomly selected states. STATDISK was used to find that the value
Stocks and Super Bowl Data Set 25 in Appendix B includes pairs of data for the Dow-Jones Industrial Average (DJIA) high value and the total number of points scored in the Super Bowl for 21 different years. Excel was used to find that the value of the linear correlation coefficient is r 5 20.133.a.
Car Sales and Sunspots Data Set 25 in Appendix B includes pairs of data for the sunspot number and the number of U.S. car sales for 21 different years. A TI-83 Plus calculator was used to find that the value of the linear correlation coefficient is r 5 20.284.a. Is there a significant linear
Fires and Acres Burned Listed below are the numbers of fires (in thousands) and the acres that were burned (in millions) in 11 western states in each year of the last decade (based on data from USA Today). Is there a correlation? The data were listed under a headline of “Loggers seize on fires to
Buying a TV Audience The New York Post published the annual salaries (in millions)and the number of viewers (in millions), with results given below for Oprah Winfrey, David Letterman, Jay Leno, Kelsey Grammer, Barbara Walters, Dan Rather, James Gandolfini, and Susan Lucci, repsectively. Is there a
Supermodel Heights and Weights Listed below are heights (in inches) and weights(in pounds) for supermodels Niki Taylor, Nadia Avermann, Claudia Schiffer, Elle MacPherson, Christy Turlington, Bridget Hall, Kate Moss, Valerie Mazza, and Kristy Hume. Is there a correlation between height and weight?
Blood Pressure Measurements Fourteen different second-year medical students took blood pressure measurements of the same patient and the results are listed below (data provided by Marc Triola, MD). Is there a correlation between systolic and diastolic values? Apart from correlation, is there some
Temperatures and Marathons In “The Effects of Temperature on Marathon Runner’s Performance” by David Martin and John Buoncristiani (Chance, Vol. 12, No. 4), high temperatures and times (in minutes) were given for women who won the New York City marathon in recent years. Results are listed
Smoking and Nicotine When nicotine is absorbed by the body, cotinine is produced.A measurement of cotinine in the body is therefore a good indicator of how much a person smokes. Listed below are the reported numbers of cigarettes smoked per day and the measured amounts of nicotine (in ng mL). (The
Tree Circumference and Height Listed below are the circumferences (in feet) and the heights (in feet) of trees in Marshall, Minnesota (based on data from “Tree Measurements” by Stanley Rice, American Biology Teacher, Vol. 61, No. 9). Is there a correlation? Why should there be a
Cereal Killers Refer to Data Set 16 in Appendix B and use the amounts of fat and the measured calorie counts. Is there a correlation?
Tobacco and Alcohol in Children’s Movies Refer to Data Set 7 in Appendix B and use the times that the animated children’s movies showed tobacco use and alcohol use. Is there a correlation between the times for tobacco and the times for alcohol?
Cholesterol and Body Mass Index Refer to Data Set 1 in Appendix B and use the cholesterol levels and body mass index values of the 40 women. Is there a correlation between cholesterol level and body mass index?
Readability Levels Refer to Data Set 14 in Appendix B and use the Flesch Reading Ease scores and the Flesch-Kincaid Grade Level values for Tom Clancy’s The Bear and the Dragon. Given that both scores are designed to measure readability, we would expect a correlation between them. Is there a
Home Selling Prices, List Prices, and Taxes Refer to Data Set 24 in Appendix B.a. Use the paired data consisting of home list price and selling price. We might expect that these variables would be related, but is there sufficient evidence to support that expectation?b. Use the paired data
Tar and Nicotine Refer to Data Set 5 in Appendix B.a. Use the paired data consisting of tar and nicotine. Based on the result, does there appear to be a significant linear correlation between cigarette tar and nicotine? If so, can researchers reduce their laboratory expenses by measuring only one
Forecasting Weather Refer to Data Set 10 in Appendix B.a. Use the five-day forecast high temperatures and the actual high temperatures. Is there a correlation? Does a significant linear correlation imply that the five-day forecast temperatures are accurate?b. Use the one-day forecast high
Florida Everglades Refer to Data Set 12 in Appendix B.a. Use the bottom temperatures and the conductivity measurements. Is there a correlation?b. Use the rainfall amounts and the conductivity measurements. Is there a correlation?c. When conductivity values are paired with measures of salinity (salt
Old Faithful Refer to Data Set 13 in Appendix B.a. Use the paired data for durations and intervals after eruptions of the geyser. Is there a significant linear correlation, suggesting that the interval after an eruption is related to the duration of the eruption?b. Use the paired data for heights
Diamond Prices, Carats, and Color Refer to Data Set 18 in Appendix B.a. Use the paired data consisting of carat (weight) and price. Is there a significant linear correlation between the weight of a diamond in carats and its price?b. Use the paired color price data. Is there a significant linear
Buying a TV Audience Find the best predicted value for the number of viewers (in millions), given that the salary (in millions of dollars) of television star Jennifer Anniston is $16 million. How does the predicted value compare to the actual number of viewers, which was 24 million?
Supermodel Heights and Weights Find the best predicted weight of a supermodel who is 69 in. tall.
Blood Pressure Measurements Find the best predicted diastolic blood pressure for a person with a systolic reading of 122.
Temperatures and Marathons Find the best predicted winning time for the 1990 marathon given that the temperature was 73 degrees. How does the predicted value compare to the actual winning time of 150.750 min?
Smoking and Nicotine Find the best predicted level of cotinine for a person who smokes 40 cigarettes per day.
Tree Circumference and Height Find the best predicted height of a tree that has a circumference of 4.0 ft. What is an advantage of being able to determine the height of a tree from its circumference?
Cereal Killers Refer to Data Set 16 in Appendix B and use the amounts of fat (x) and the measured calorie counts (y). Find the best predicted calorie count for a cereal with 0.05 grams of fat per gram of cereal.
Tobacco and Alcohol in Children’s Movies Refer to Data Set 7 in Appendix B and use the times that the animated children’s movies showed tobacco use (x) and alcohol use (y). Find the best predicted time for alcohol use, given that a movie does not show any tobacco use.
Cholesterol and Body Mass Index Refer to Data Set 1 in Appendix B and use the cholesterol levels (x) and body mass index values (y) of the 40 women. What is the best predicted value for the body mass index of a woman having a cholesterol level of 500?
Readability Levels Refer to Data Set 14 in Appendix B and use the Flesch Reading Ease scores (x) and the Flesch-Kincaid Grade Level values (y) for Tom Clancy’s The Bear and the Dragon. Find the best predicted Flesch-Kincaid Grade Level value for a page with a Flesch Reading Ease score of 50.0.
Home Selling Prices, List Prices, and Taxes Refer to Data Set 24 in Appendix B.Caution: The sample values of list prices and selling prices are in thousands of dollars, but the tax amounts are in dollars.a. Use the paired data consisting of home list price (x) and selling price (y). What is the
Tar and Nicotine Refer to Data Set 5 in Appendix B.a. Use the paired data consisting of tar (x) and nicotine (y). What is the best predicted nicotine level for a cigarette with 15 mg of tar?b. Use the paired data consisting of carbon monoxide (x) and nicotine (y). What is the best predicted
Forecasting Weather Refer to Data Set 10 in Appendix B.a. Use the five-day forecast high temperatures (x) and the actual high temperatures(y). What is the best predicted actual high temperature if the five-day forecast high temperature is 28°?b. Use the one-day forecast high temperatures (x) and
Florida Everglades Refer to Data Set 12 in Appendix B.a. Use the bottom temperatures (x) and the conductivity measurements (y). What is the best predicted conductivity measurement for a time when the bottom temperature is 30.0°C?b. Use the rainfall amounts (x) and the conductivity measurements
Old Faithful Refer to Data Set 13 in Appendix B.a. Use the paired data for durations (x) and intervals (y) after eruptions of the geyser.What is the best predicted time before the next eruption if the previous eruption lasted for 210 sec?b. Use the paired data for heights of eruptions (x) and
Diamond Prices, Carats, and Color Refer to Data Set 18 in Appendix B.a. Use the paired data consisting of the carat weight (x) and the price (y). What is the best predicted price of a diamond with a weight of 1.5 carats?b. Use the paired color (x) and price (y) data. What is the best predicted
Identifying Outliers and Influential Points Refer to the sample data listed in Table 9-1. If we include another pair of values consisting of x 5 120 (for 1,200,000 boats)and y 5 160 (manatee deaths from boats), is the new point an outlier? Is it an influential point?
Identifying Outliers and Influential Points Refer to the sample data listed in Table 9-1. If we include another pair of values consisting of x 5 120 (for 1,200,000 boats)and y 5 10 (manatee deaths from boats), is the new point an outlier? Is it an influential point?9-3 Beyond the Basics
How Is a Regression Equation Affected by Change in Scale? Large numbers, such as those in the accompanying table, often cause computational problems. First use the given data to find the equation of the regression line, then find the equation of the regression line after each x-value has been
Testing Least-Squares Property According to the least-squares property, the regression line minimizes the sum of the squares of the residuals. We noted that with the paired data in the margin, the regression equation is 5 5 1 4x and the sum of the squares of the residuals is 364. Show that the
Using Logarithms to Transform Data If a scatterplot reveals a nonlinear (not a straight line) pattern that you recognize as another type of curve, you may be able to apply the methods of this section. For the data given in the margin, find the linear equation (y 5 b0 1 b1x) that best fits the
Equivalent Hypothesis Tests Explain why a test of the null hypothesis H0: r 5 0 is equivalent to a test of the null hypothesis H0: b1 5 0 where r is the linear correlation coefficient for a population of paired data, and b1 is the slope of the regression line for that same population.
Residual Plot A scatterplot is a plot of the paired (x, y) sample data. A residual plot is a graph of the points with the same x-coordinates, but the corresponding y-coordinates are the residual values. To construct a residual plot, use the same x-axis as the scatterplot, but use a vertical axis of
Finding Predicted Value and Prediction Interval Refer to Exercise 10 and assume that the necessary conditions of normality and variance are met.a. Find the predicted diastolic reading given that the systolic reading is 120.b. Find a 95% prediction interval estimate of the diastolic reading given
Finding Predicted Value and Prediction Interval Refer to the data given in Exercise 11 and assume that the necessary conditions of normality and variance are met.a. Find the predicted height of a tree that has a circumference of 4.0 ft.b. Find a 99% prediction interval estimate of the height of a
Finding Predicted Value and Prediction Interval Refer to the data described in Exercise 12 and assume that the necessary conditions of normality and variance are met.a. Find the predicted Flesch Reading Ease score for a page that has an average of 4.0 characters per word.b. Find a 99% prediction
Understanding Variationa. If a collection of paired data includes at least three pairs of values, what do you know about the linear correlation coefficient if se 5 0?b. If a collection of paired data is such that the total explained variation is 0, what do you know about the slope of the regression
Understanding Variationa. Find an expression for the unexplained variation in terms of the sample size n and the standard error of estimate se.b. Find an expression for the explained variation in terms of the coefficient of determination r 2 and the unexplained variation.c. Suppose we have a
Finding Confidence Interval for Mean Predicted Value From the expression given in this section for the margin of error corresponding to a prediction interval for y, we can get the expression which is the standard error of the prediction when predicting for a single y, given that x 5 x0. When
If only one independent variable is used to predict the city fuel consumption amount(in mi gal), which single variable is best? Why?
If exactly two independent variables are to be used to predict the city fuel consumption amount, which two variables should be chosen? Why?
Which regression equation is best for predicting the city fuel consumption amount?Why?
If a car has a highway fuel consumption rate of 35 mi gal, a weight of 2675 lb, and an engine displacement of 3.8 L, what is the best predicted value of city fuel consumption rate? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?
Heights of Parents and Children Refer to Data Set 2 in Appendix B.a. Find the regression equation that expresses the dependent variable of a child’s height in terms of the independent variable of the height of the mother.b. Find the regression equation that expresses the dependent variable of a
Readability of Harry Potter Refer to Data Set 14 in Appendix B and use the values for J. K. Rowling’s Harry Potter and the Sorcerer’s Stone.a. Find the regression equation that expresses the dependent variable of Flesch Reading Ease score in terms of the independent variable of the words per
Cereal and Calories Refer to Data Set 16 in Appendix B.a. Find the regression equation that expresses the dependent variable of calories in terms of the independent variable of the amount of fat.b. Find the regression equation that expresses the dependent variable of calories in terms of the
Using Garbage to Predict Population Size Refer to Data Set 23 in Appendix B.a. Find the regression equation that expresses the dependent variable of household size in terms of the independent variable of the weight of discarded food.b. Find the regression equation that expresses the dependent
Cigarette Nicotine: Finding Best Multiple Regression Equation Refer to Data Set 5 in Appendix B and find the best multiple regression equation with nicotine as the dependent variable. Is this “best” equation good for predicting the amount of nicotine in a cigarette based on the amount of tar
Price of a Diamond: Finding Best Multiple Regression Equation Refer to Data Set 18 in Appendix B.a. Using only the traditional “three C’s” of carat, color, and clarity, find the best multiple regression equation that could be used to predict the price of a diamond.b. The variables of depth
Home Selling Price: Finding Best Multiple Regression Equation Refer to Data Set 24 in Appendix B and find the best multiple regression equation with selling price as the dependent variable. Is this “best” equation good for predicting the selling price of a home?
Using Multiple Regression for Equation of Parabola In some cases, the best-fitting multiple regression equation is of the form 5 b0 1 b1x 1 b2x2. The graph of such an equation is a parabola. Using the data set listed in the margin, let x1 5 x, let x2 5 x2, and find the multiple regression equation
Stock Market Refer to the annual high values of the Dow-Jones Industrial Average that are listed in Data Set 25 in Appendix B. What is the best predicted value for the year 2001? Given that the actual high value in 2001 was 11,350, how good was the predicted value? What does the pattern suggest
Target Stores The accompanying table lists the number of Target department stores in the United States (based on data from Target). What is the best predicted value for the number of Target stores in 2005?
Return on Investment Kendra Korbin, owner and operator of the Cyber Video Game Store, records her business costs and revenue for different years, with the results listed below.9-6 Beyond the Basics
Moore’s Law In 1965, Intel co-founder 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. Here are data describing the number of transistors (in thousands) for different
Using the Sum of Squares Criterion It was noted that 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. A residual is the difference between an observed y value and the value of y predicted from the model, which is
DWI and Jail A study was conducted to investigate the relationship between age (in years) and BAC (blood alcohol concentration) measured when convicted DWI (driving while intoxicated) jail inmates were first arrested. Sample data are given below for randomly selected subjects (based on data from
Tipping Many of us have heard that the tip should be 15% of the bill. The accompanying table lists some sample data collected from the author’s students. Use the sample data for the following.a. Is there sufficient evidence to conclude that there is a relationship between the amount of the bill
a. Use a 0.05 significance level to test for a linear correlation between consumption and price.b. What percentage of the variation in price can be explained by the linear relationship between price and consumption?c. Find the equation of the regression line that expresses consumption (y) in terms
a. Use a 0.05 significance level to test for a linear correlation between consumption and income.b. What percentage of the variation in consumption can be explained by the linear relationship between consumption and income?c. Find the equation of the regression line that expresses consumption (y)
a. Use a 0.05 significance level to test for a linear correlation between consumption and temperature.b. What percentage of the variation in consumption can be explained by the linear relationship between consumption and temperature?c. Find the equation of the regression line that expresses
Use software such as STATDISK or Minitab or Excel to find the multiple regression equation of the form 5 b0 1 b1x1 1 b2x2 1 b3x3, where the dependent variable y represents consumption, x1 represents price, x2 represents income, and x3 represents temperature. Also identify the value of the multiple
Leo Tolstoy’s War and Peace Refer to the sample data from 12 randomly selected pages from Leo Tolstoy’s War and Peace as listed in Data Set 14 in Appendix B.a. The Flesch Reading Ease scores and the Flesch-Kincaid Grade Level scores are both designed to measure readability. Test for a
Effects of Heredity and Environment on IQ In studying the effects of heredity and environment on intelligence, it has been helpful to analyze the IQs of identical twins who were separated soon after birth. Identical twins share identical genes inherited from the same fertilized egg. By studying
a. A set of data is at the nominal level of measurement and you want to obtain a representative data value. Which of the following is most appropriate: mean, median, mode, or midrange? Why?b. A sample is obtained by telephoning the first 250 people listed in the local telephone directory. What type
Wristwatch Errors As part of a project for a statistics class, a student collects data on wristwatch accuracy. The following error times (in seconds) are obtained. (Positive values represent watches that are ahead of the correct time, and negative values represent watches that are behind the
Air Passenger Complaints In a recent year, there were 23,000 complaints filed by air passengers. The complaint categories and frequencies provided by the Department of Transportation are as follows: customer care (4370); problems with the flight (9200);reservations, ticketing, boarding (1610);
Transforming Data A statistics professor has found that the times used by students on her final exam have a mean of 135 minutes and a standard deviation of 15 minutes.She plans to add a new question that will require 5 additional minutes from each student.a. What is the mean after the new question
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