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Elementary Statistics 10th Edition Mario F. Triola - Solutions

8. The mean and standard deviation from Exercise 7 are sample statistics, but treat them as population parameters for a normally distributed population, and find the probability that a random Super Bowl game will have less than 40 total points scored.
7. Find the mean and standard deviation of the sample of Super Bowl points.
6. Do the Super Bowl points appear to come from a population with a normal distribution?Why or why not?
5. Why would it be a bad idea to try to estimate the next consecutive DJIA high value by constructing a confidence interval estimate of the DJIA values?
4. Construct a 95% confidence interval estimate for the mean number of points scored in Super Bowl games.
3. Is it possible to test the claim that the mean number of points scored in the Super Bowl is equal to the mean value of the DJIA? Would such a test make sense?
2. Find the regression equation in which the DJIA high value is the response (y) variable.What is the best predicted DJIA value for a year in which there are 50 points scored in the Super Bowl?
1. Test for a correlation between Super Bowl points and the DJIA. Is the result as you expected?
5. Use software such as STATDISK, Minitab, or Excel to find the multiple regression equation of the form , where the response variable y represents cost, x1 represents electricity consumption in kWh, and x2 represents average daily temperature. Also identify the value of the multiple coefficient of
4.a. Use a 0.05 significance level to test for a linear correlation between the average daily temperature and the cost.b. What percentage of the variation in cost can be explained by the linear relationship between cost and average daily temperature?c. Find the equation of the regression line that
3.a. Use a 0.05 significance level to test for a linear correlation between the cost of electricity and the kWh of electricity consumed.b. What percentage of the variation in cost can be explained by the linear relationship between electricity consumption (in kWh) and cost?c. Find the equation of
2. Old Faithful Use the data given below (from Table 10-1). The duration times are in seconds and the heights are in feet.a. Is there a significant linear correlation between duration of an eruption of the Old Faithful geyser and the height of the eruption?b. Find the equation of the regression
1. Manatee Deaths The table below lists the number of Florida manatee deaths related to encounters with watercraft and natural causes for each of several different years(based on data from Florida Fish and Wildlife Conservation).a. Find the value of the linear correlation coefficient and determine
4. Predictions After finding that there is a significant linear correlation between two variables, a predicted value of y is obtained by using the regression equation. Given that there is a significant linear correlation, will the projected value be very accurate?
3. Causation A medical researcher finds that there is a significant linear correlation between the amount of a drug taken and the cholesterol level of the subject. Is she justified in writing in a journal article that the drug causes lower cholesterol levels? Why or why not?
2. Correlation Given a collection of paired data, the linear correlation coefficient is found to be r 0. Does that mean that there is no relationship between the two variables?
1. Correlation and Regression In your own words, describe correlation, regression, and the difference between them.
15. Using the Sum of Squares Criterion 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 denoted as . Better
14. Population in 2050 When the exercises in this section were written, the United Nations used its own model to predict a population of 394 million for the United States in 2050. Based on the data in Table 10-4, which of the models discussed in Section 10-6 yields a projected population closest to
c. Compare the results from parts (a) and (b). Does Moore’s law appear to be working reasonably well?
b. Which mathematical model best fits the listed sample data?
a. Assuming that Moore’s law is correct and transistors double every 18 months, which mathematical model best describes this law: linear, quadratic, logarithmic, exponential, power? What specific function describes Moore’s law?
13. 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. The table below lists the number of transistors (in thousands) for different
12. Stock Market Listed below in order by row are the annual high values of the Dow Jones Industrial Average for each year beginning with 1980. What is the best predicted value for the year 2004? Given that the actual high value in 2004 was 10,855, how good was the predicted value? What does the
11. Physics Experiment An experiment in a physics class involves dropping a golf ball and recording the distance (in meters) it falls for different times (in seconds) after it was released. The data are given in the table below. Project the distance for a time of 12 sec, given that the golf ball is
10. Manatee Deaths from Natural Causes The accompanying table lists the number of Florida manatee deaths from natural causes (based on data from Florida Fish and Wildlife Conservation). Does the best model appear to be a reasonably good model?Year 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992
9. Manatee Deaths from Boats The accompanying table lists the number of Florida manatee deaths related to encounters with watercraft (based on data from Florida Fish and Wildlife Conservation).x 1 2 3 4 5 6 y 5 7 9 11 13 15 x 1 2 3 4 5 6 y 2 4 8 16 32 64 x 1 2 3 4 5 6 y 1 7 17 31 49 71 x 1 2 3 4 5
4. Best Model Assume that we use a sample with the methods of this section to find that among the five different possible models, the best model is y 4x1.2 with R2 0.200.Does this best model appear to be a good model? Why or why not?Finding the Best Model. In Exercises 5–12, construct a
3. Projections In this section we used the population values from the year 1800 to the year 2000, and we found that the best model is described by y 2.77x2 6.00x 10.01, where the population value of y is in millions. What is wrong with using this model to project the population size for the
2. R2 How are values of R2 used to compare different models being considered?
1. Model What is a mathematical model?
16. Appendix B Data Set: Old Faithful This section used the Old Faithful data from 8 eruptions, as listed in Table 10-1. Refer to Data Set 11 in Appendix B and use the complete data set from 40 eruptions. Determine the best multiple regression equation that expresses the response variable (y) of
15. Appendix B Data Set: Home Selling Price Refer to Data Set 18 in Appendix B and find the best multiple regression equation with selling price as the response (y) variable.Is this “best” equation good for predicting the selling price of a home?
14. Appendix B Data Set: Using Garbage to Predict Population Size Refer to Data Set 16 in Appendix B.a. Find the regression equation that expresses the response variable (y) of household size in terms of the predictor variable of the weight of discarded food.b. Find the regression equation that
13. Appendix B Data Set: Predicting Nicotine in Cigarettes Refer to Data Set 3 in Appendix B.a. Find the regression equation that expresses the response variable (y) of nicotine amount in terms of the predictor variable (x) of the tar amount.b. Find the regression equation that expresses the
12. If a male has a height of 72 in., a waist circumference of 105 cm, and a cholesterol level of 250 mg, what is the best predicted value of his weight? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?
11. Which regression equation is best for predicting the weight? Why?
26. 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 get which is the standard error of the prediction when predicting for a single y, given that x x0. When predicting for the mean of
Finding a Prediction Interval. In Exercises 21–24, refer to the Table 10-1 sample data.Let x represent the duration time (in seconds) and let y represent the time interval (in minutes) after the eruption to the next eruption. Use the given duration time and the given confidence level to construct
20. Finding Predicted Value and Prediction Interval Refer to the data described in Exercise 16 and assume that the necessary conditions of normality and variance are met.a. Find the predicted temperature when a cricket chirps 1000 times in 1 min.b. Find a 99% prediction interval estimate of the
19. Finding Predicted Value and Prediction Interval Refer to the data given in Exercise 15 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
18. Finding Predicted Value and Prediction Interval Refer to Exercise 14 and assume that the necessary conditions of normality and variance are met.a. Find the predicted gross amount for a movie with a budget of $100 million.b. Find a 95% prediction interval estimate of the gross amount for a movie
17. Effect of Variation on Prediction Interval Refer to the data given in Exercise 13 and assume that the necessary conditions of normality and variance are met.a. Find the predicted fuel consumption rate for a car that weighs 3700 lb.b. Find a 95% prediction interval estimate of the fuel
16. Crickets and Temperature One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute.Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees Fahrenheit (based on data from The
15. 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).Systolic 138 130 135 140 120 125 120 130 130 144 143 140 130 150 Diastolic 82 91 100 100 80 90 80
14. Movie Budgets and Gross Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies (based on data from the Motion Picture Association of America).Budget 62 90 50 35 200 100 90 Gross 65 64 48 57 601 146 47
13. Car Weight and Fuel Consumption Listed below are the weights (in pounds) and the highway fuel consumption amounts (in mi gal) of randomly selected cars (Chrysler Sebring, Ford Mustang, BMW 3-Series, Ford Crown Victoria, Honda Civic, Mazda Protégé, Hyundai Accent).>Minitab Weight 3175 3450
12. Finding Prediction Interval For a given tar amount of 17 mg, identify the 95% prediction interval estimate of the amount of nicotine, and write a statement interpreting that interval.Finding Measures of Variation. In Exercises 13–16, find the (a) explained variation, (b)unexplained variation,
11. Predicting Nicotine Amount If a cigarette has 17 mg of tar, what is the single value that is the best predicted amount of nicotine? (Assume that there is a linear correlation between tar and nicotine.)
. Identifying Total Variation What percentage of the total variation in nicotine can be explained by the linear relationship between tar and nicotine?
9. Testing for Correlation Use the information provided in the display to determine the value of the linear correlation coefficient. Given that there are 29 pairs of data, is there a linear correlation between the amount of tar and the amount of nicotine in a cigarette?
4. Explained and Unexplained Variation What is the difference between explained variation and unexplained variation?Interpreting the Coefficient of Determination. In Exercises 5–8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of
3. Explained Deviation and Variation What is the difference between explained deviation and explained variation?
2. Coefficient of Determination What is a coefficient of determination in general? What is the coefficient of determination for r 0.400? What practical information does it give us?
1. Prediction Interval Use your own words to describe a prediction interval.
36. Residual Plot Consider the data in the table below.a. Examine the data and identify the relationship between x and y.b. Find the linear correlation coefficient and use it to determine whether there appears to be a significant linear correlation between x and y.c. Construct a scatterplot. What
35. 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 yˆ 5 8 1 3x yˆ 5 5 1 4x H0: b1 5 0>x 1 2 4
34. 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 and the sum of the squares of the residuals is 364. Show that the equation
33. Equivalent Hypothesis Tests Explain why a test of the null hypothesis H0: r 0 is equivalent to a test of the null hypothesis 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.
32. Appendix B Data Set: Forecast and Actual Temperatures Refer to Data Set 8 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 70 degrees?b. Use the
31. Appendix B Data Set: Bad Stuff in Cigarettes Refer to Data Set 3 in Appendix B.a. Use the paired data consisting of tar (x) and nicotine (y). What is the best predicted nicotine content of a cigarette with 15 mg of tar?b. Use the paired data consisting of carbon monoxide (x) and nicotine (y).
30. Appendix B Data Set: Discarded Plastic and Household Size Refer to Data Set 16 in Appendix B and use the weights of discarded plastic and the corresponding household sizes. Find the best predicted household size given that the household discards 5.00 lb of plastic.
29. Appendix B Data Set: List Price and Selling Price Refer to Data Set 18 in Appendix B and use the list prices and selling prices of homes sold. Find the best predicted selling price of a home having a list price of $400,000.
28. State Budget and Days Late Find the best predicted number of days that a New York State budget is late, given that the size of the budget is $104 billion. (In the data given below, the budget amounts are in billions of dollars.)Budget Number of Days Late 101 96 91 85 80 73 71 66 63 63 133 44 45
27. Height and Pulse Rate Find the best predicted pulse rate for a woman who is 66 in.tall.Height (in.) Pulse Rate (beats min)64.3 66.4 62.3 62.3 59.6 63.6 76 72 88 60 72 68 59.8 63.3 67.9 61.4 66.7 64.8 80 64 68 68 80 76
26. Fires and Acres Burned Find the best predicted number of acres burned given that there were 50 thousand fires. (In the table below, the numbers of fires are in thousands and acres are in millions.)Fires 73 69 58 48 84 62 57 45 70 63 48 Acres burned 6.2 4.2 1.9 2.7 5.0 1.6 3.0 1.6 1.5 2.0 3.7
25. Crickets and Temperature Find the best predicted temperature for a time when a cricket is chirping at the rate of 1000 chirps per minute.Chirps in 1 min 882 1188 1104 864 1200 1032 960 900 Temperature (F) 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6
24. Parent Child Heights Find the best predicted height of a daughter to be born to a mother who is 66 in. tall.>Mother’s height 63 67 64 60 65 67 59 60 Daughter’s height 58.6 64.7 65.3 61.0 65.4 67.4 60.9 63.1
23. Temperatures and Marathons Find the best predicted winning time for the 1990 marathon when the temperature was 73 degrees. How does that predicted winning time compare to the actual winning time of 150.750 min?x (temperature) 55 61 49 62 70 73 51 57 y (time) 145.283 148.717 148.300 148.100
22. Smoking and Nicotine Find the best predicted cotinine level for a person who smokes 40 cigarettes per day.x (cigarettes per day) 60 10 4 15 10 1 20 8 7 10 10 20 y (cotinine) 179 283 75.6 174 209 9.51 350 1.85 43.4 25.1 408 344
21. Buying a TV Audience Find the best predicted number of viewers for a television star with a salary of $2 million. (In the table below, the salaries are in millions of dollars and the numbers of viewers are in millions.)Salary 100 14 14 35.2 12 7 5 1 Viewers 7 4.4 5.9 1.6 10.4 9.6 8.9 4.2
20. Murders and Population Size Find the best predicted population size for a city with 120 murders. (The population sizes are in hundreds of thousands.)Murders 258 264 402 253 111 648 288 654 256 60 590 Population 4 6 9 6 3 29 15 38 20 6 81
19. Blood Pressure Measurements Find the best predicted diastolic blood pressure for a person with a systolic reading of 140.Systolic 138 130 135 140 120 125 120 130 130 144 143 140 130 150 Diastolic 82 91 100 100 80 90 80 80 80 98 105 85 70 100
18. Supermodel Heights and Weights Find the best predicted weight of a supermodel who is 72 in. tall.Chest size 26 45 54 49 35 41 41 49 38 31 Weight 80 344 416 348 166 220 262 360 204 144 Height (in.) 70 70.5 68 65 70 70 70 70 71 Weight (lb) 117 119 105 115 119 127 113 123 115
17. Bear Chest Size and Weight Find the best predicted weight (in pounds) of a bear with a chest size of 50 in.
16. Car Weight and Fuel Consumption Find the best predicted highway fuel consumption amount (in mi>gal) for a car that weighs 3000 lb.Weight 3175 3450 3225 3985 2440 2500 2290 Fuel 27 29 27 24 37 34 37 consumption
15. Movie Budgets and Gross Find the best predicted gross amount for a movie with a budget of 40 million dollars. (In the table below, all amounts are in millions of dollars.)Budget 62 90 50 35 200 100 90 Gross 65 64 48 57 601 146 47
14. Song Audiences and Sales Find the best predicted number of albums sold for a song with 20 (hundred million) audience impressions. (In the table below, audience impressions are in hundreds of millions and the numbers of albums sold are in hundreds of thousands).Audience impressions 28 13 14 24
13. Old Faithful Find the best predicted time of the interval after an eruption (to the next eruption) given that the current eruption has a height of 100 ft.x 0 2 1 4 8 y 6 5 4 0 6 Height 140 110 125 120 140 120 125 150 Interval after 92 65 72 94 83 94 101 87
12. Effects of Clusters Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-2.a. Using the pairs of values for all 8 points, find the equation of the regression line.b. Using only the pairs of values for the four points in the lower left corner, find the equation of the
11. Effects of an Outlier Refer to the Minitab-generated scatterplot given in Exercise 11 of Section 10-2.a. Using the pairs of values for all 10 points, find the equation of the regression line.b. After removing the point with coordinates (10, 10), use the pairs of values for the remaining nine
9.yˆ 5 53.3 2 0.000442x, yˆ 5 3.46 1 1.01x, yˆ 5 23.22 1 1.02x, yˆ 5 23.22 1 1.02x, x 1 1 2 5 3 y 0 2 2 3 5 10-3 Regression 553 554 Chapter 10 Correlation and Regression 10.
8. Stocks and Super Bowl The Dow Jones Industrial Average (DJIA) high value and the total number of points scored in the Super Bowl were recorded for 21 different years.Excel was used to find that the value of the linear correlation coefficient is r0.133 and the regression equation is where x is
7. Sugar and Calories in Cereal The author collected data from 16 cereals consisting of the sugar contents (in grams per gram of cereal) and the calories (per gram of cereal).STATDISK was used to find that the linear correlation coefficient is r 0.765 and the equation of the regression line is
6. IQ Scores of Adopted Children Living Together IQ scores were obtained from randomly selected adopted children living together. For 20 such pairs of children, the linear correlation coefficient is 0.027 and the equation of the regression line is where x represents the IQ score of the older child.
5. IQ Scores of Twins Separated at Birth IQ scores were obtained from randomly selected twins separated at birth. For 20 such twins, the linear correlation coefficient is 0.870 and the equation of the regression line is where x represents the IQ score of the twin that was born first. Also, the 20 x
4. Requirements Are the requirements for regression analysis identical to the requirements for correlation analysis? If not, how do the requirements differ?Making Predictions. In Exercises 5–8, use the given data to find the best predicted value of the dependent variable. Be sure to follow the
3. Predictions Why is it unwise to use a regression equation for predicting a value of y by using a value of x that is far beyond the scope of the available sample data?
2. Best-Fitting Line In what sense is the regression line the straight line that “best” fits the points in a scatterplot?
1. Predictor and Response Variables What is a predictor variable? What is a response variable? Why do you suppose that they were given those particular names?
40. Power of a Test A sample of size n 5 36 is used with a 0.05 significance level to test the null hypothesis of r 5 0 against the alternative hypothesis of r 0. If the population actually has a correlation coefficient of r 5 0.55, the value of b is 0.06. What does that value of b indicate? What
39. Constructing Confidence Intervals for r When obtaining samples of n paired values from a population with a correlation coefficient of r, the distribution of linear correlation coefficients r is not a normal distribution, but values of have a distribution that is approximately normal with mean
37. Correlations with Transformed Data In addition to testing for a linear correlation between x and y, we can often use transformations of data to explore for other relationships.For example, we might replace each x value by x2 and use the methods of this section to determine whether there is a
36. Given: There is a linear correlation between state average tax burdens and state average incomes.Conclusion: There is a linear correlation between individual tax burdens and individual incomes.10-2 BEYOND THE BASICS
35. Given: Subjects take a test of verbal skills and a test of manual dexterity, and those pairs of scores result in a linear correlation coefficient very close to 0.Conclusion: Scores on the two tests are not related in any way.
34. Given: There is a linear correlation between personal income and years of education.Conclusion: More education causes a person’s income to rise.
33. Given: The paired sample data of the ages of subjects and their scores on a test of reasoning result in a linear correlation coefficient very close to 0.Conclusion: Younger people tend to get higher scores.
32. Appendix B Data Set: Forecast and Actual Temperatures Refer to Data Set 8 in Appendix B.a. Use the five-day forecast high temperatures and the actual high temperatures. Is there a correlation? Does a linear correlation imply that the five-day forecast temperatures are accurate?10-2 Correlation
c. Assume that researchers want to develop a method for predicting the amount of nicotine, and they want to measure only one other variable. In choosing between tar and carbon monoxide, which is the better choice? Why?
31. Appendix B Data Set: Cigarette Tar and Nicotine Refer to Data Set 3 in Appendix B.a. Use the paired data consisting of tar and nicotine. Based on the result, does there appear to be a linear correlation between cigarette tar and nicotine? If so, can researchers reduce their laboratory expenses

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