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Elementary Statistics 3rd Canadian Edition Mario F. Triola - Solutions

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 x1 and use the methods of this section to determine whether there is a linear correlation between y and x2.
The critical values of r in Table A-6 are found by solvingfor r to get where the t value is found from Table A-3 by assuming a two-tailed case with n - 2 degrees of freedom. Table A-6 lists the results for selected values of n and a. Use the formula for r given here and Table A-3 (with n - 2
Given n pairs of data from which the linear correlation coefficient r can be found, use the following procedure to construct a confidence interval about the population parameter p.Step a. Use Table A-2 to find za/2 that corresponds to the desired degree of confidence.Step b. Evaluate the interval
Refer to Table 11-1, used for the chapter problem. This table includes paired data representing the recorded latitudes and magnitudes of seismic activity (earthquakes). These data can only be recorded if an earthquake is picked up by monitors, and the great majority of these are located in Canada's
(a) use a scatter plot to determine whether there is a significant linear correlation between x and y, and (b) find the values of n, 1.x, 1x2, C^x)2, Ixy, and the linear correlation coefficient r.
(a) use a scatter plot to determine whether there is a significant linear correlation between x and y, and (b) find the values of n, 1.x, 1x2, C^x)2, Ixy, and the linear correlation coefficient r.In Exercises 5-18, a. Construct the scatter plot. b. Find the value of the linear correlation
When bears were anesthetized, researchers measured the distances (in inches) around their chests and they weighed the bears (in pounds). The results are given below for 8 male bears. Based on the results, does a bear's weight seem to be related to its chest size? Do the results change if the chest
The accompanying table lists the number of Christmas trees (in thousands) exported from New Brunswick in one year and the dollar value (also in thousands) of those exports. Based on the results, can New Brunswick depend on receiving a greater dollar value for tree exports when it exports more
The accompanying table lists weights (in kilograms) of plastic discarded by a sample of households, along with the sizes of the households (adapted from Data Set 1). Is there a significant linear correlation? This issue is important because the presence of a correlation implies that Statistics
The paired data below consist of weights (in kilograms) of discarded paper and sizes of the households.
A study was conducted to compare the incubation periods and fledgling periods (in days) of different bird species. Sample data are given below for randomly selected species.a. Do the incubation and fledgling periods appear to be related?b. Each of the numbers shown in the table is itself a mean-for
Use the given data to find the equation of the regression line.
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.Data from Management Information Circular, January 26, 2001, TWIN
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.The salaries in the accompanying table are shown in thousands of
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.What is the best predicted profit margin (as a percent) for a
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.Refer to Data Set 16 in Appendix B.a. Use the paired duration and
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.Refer to Data Set 4 in Appendix B and use the paired columns for
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section. Refer to Data Set 21 in Appendix B. a. Use the paired data
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.Refer to Data Set 4 in Appendix B and use the paired columns for
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.Refer to Data Set 7 of Appendix B and use the paired data
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.What is the best predicted revenue for a top company that employs
In each of the following cases, find the best predicted value of y given that x = 3.00. The given statistics are summarized from paired sample data. a. r = 0.931, y = 7.00, n = 10, and the equation of the regression line is = 4.00 + 2.00x. b. r = -0.033, y - 2.50, n = 80, and the equation of the
Use the given data to find the equation of the regression line.
In each of the following cases, find the best predicted value of y given that x = 2.00. The given statistics are summarized from paired sample data.a. r = -0.882, y = 3.57, n = 15, and the equation of the regression line is = 23.00 - 8.00*.b. r = 0.187, y = 9.33, n - 60, and the equation of the
Refer to these data for Parliaments of up to 3 years' duration. If there were an additional Parliament to include, which lasted 1 year and was in session for 364 days, would the new point be an outlier? Would it be an influential point?
Refer to the 13 pairs of data listed in Table 11-1. If we include a 14th data point, for an earthquake at 85°N latitude with magnitude 75ML, is the new point an outlier? Is it an influential point?
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 divided by 1000. How are the results affected by the change in
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 y = 5 + 4x and the sum of the squares of the residuals is 364. Show that the equation y = 8 + 3x results in a
If the scatter plot 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 = b0 + bxx) that best fits the sample data, and find the logarithmic
Explain why a test of the null hypothesis HQ: p - 0 is equivalent to a test of the null hypothesis HQ: /3, = 0, where p is the linear correlation coefficient for a population of paired data, and /3, is the slope of the regression line for that same population.
See Data Set 19 in Appendix B. If you draw a scatter plot to compare (y) the maximum life spans of the first six animals listed with (x) their metabolic rates, there appears to be a nonlinear relationship. For those data, find the linear equation (y = bQ + b{x) that best fits the sample data. Then
Use the given data to find the equation of the regression line.
Use the given data to find the equation of the regression line.
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.What is the best predicted size of a household that discards 5.00
Find the regression equation; unless the problem suggests otherwise, let the first variable be the independent (x) variable. Caution: When finding predicted values, be sure to follow the prediction procedure described in this section.What is the best predicated value for this mining stock, if the
The value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the regression line. r = 0.2
Refer to Exercise 6 and assume that the necessary conditions of normality and variance are met.a. For a bear with a chest size of 52 in., find y, the predicted weight.b. Find the 99% prediction interval of y for x = 52.
Refer to the data given in Exercise 7 and assume that the necessary conditions of normality and variance are met.a. Find the predicted size of a household that discards 1.25 kg of plastic.b. Find the 95% prediction interval for the size of a household that discards 1.25 kg of plastic.
Refer to the data given in Exercise 8, and assume that the necessary conditions of normality and variance are met. a. For a year that the TSE 300 closes at 14,447.99, find the predicted closing price for the mining stock. b. Find the 99% prediction interval for the closing price of the mining
Refer to the data in Exercise 11 in Section 11-3. Let x represent the number of years of a person's education, and let y represent his or her salary (in thousands of dollars). Construct a prediction interval estimate of the salary of a person who has the given years of education. Use the given
Refer to the data in Exercise 11 in Section 11-3. Let x represent the number of years of a person's education, and let y represent his or her salary (in thousands of dollars). Construct a prediction interval estimate of the salary of a person who has the given years of education. Use the given
Refer to the data in Exercise 11 in Section 11-3. Let x represent the number of years of a person's education, and let y represent his or her salary (in thousands of dollars). Construct a prediction interval estimate of the salary of a person who has the given years of education. Use the given
Refer to the data in Exercise 11 in Section 11-3. Let x represent the number of years of a person's education, and let y represent his or her salary (in thousands of dollars). Construct a prediction interval estimate of the salary of a person who has the given years of education. Use the given
Confidence intervals for the y-intercept of a regression line (y = (30 + /3,x) can be found by evaluating the limits in the intervals below:In these expressions, the y-intercept b0 is found from the sample data and t a/2 is found from Table A-3 by using n - 2 degrees of freedom. Using the
a. If a collection of paired data includes at least three pairs of values, what do you know about the linear correlation coefficient if se = 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 line?
a. Find an expression for the unexplained variation in terms of the sample size n and the standard error of estimate s .eb. Find an expression for the explained variation in terms of the coefficient of determination r2 and the unexplained variation.c. Suppose we have a collection of paired data for
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the regression line. r = -0.6
In constructing a confidence interval for the mean value of y for a mathematical model based on a natural log transformation of y, the initial confidence interval is:- E + E which we can thenWhich we can then transform back to the original units:e{ - E) + E)In the example of the wood density being
An alternate approach to calculating standard errors and confidence intervals for regression is to apply them to the calculated bQ and x coefficient(s), instead of to the y estimate. For example, this is part of Excel's regression output for comparing the weights and lengths of bears. This shows
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the regression line. r = -0.225
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the regression line. r = 0.837
Find the(a) Explained variation,(b) Unexplained variation,(c) Total variation,(d) Coefficient of determination, and(e) Standard error of estimate se.The accompanying table lists numbers x of patio tiles and costs y (in dollars) of having them manually cut to fit. (The equation of the regression
Find the(a) Explained variation,(b) Unexplained variation,(c) Total variation,(d) Coefficient of determination, and(e) Standard error of estimate se.The paired data below consist of the chest sizes (in inches) and weights (in pounds) of a sample of male bears. (The equation of the regression line
Find the(a) Explained variation,(b) Unexplained variation,(c) Total variation,(d) Coefficient of determination, and(e) Standard error of estimate se.The paired data below consist of the weights (in kilograms) of discarded plastic and sizes of households. (The equation of the regression line, for
Find the(a) Explained variation,(b) Unexplained variation,(c) Total variation,(d) Coefficient of determination, and(e) Standard error of estimate se.The paired data below consist of annual closing values of the TSE 300 stock index and of corresponding closing prices for a Canadian mining stock.
Refer to the data given in Exercise 5 and assume that the necessary conditions of normality and variance are net.a. For x = 4, find y, the predicted value of y.b. How does the value of se affect the construction of the 95% prediction interval of y for x = 4?
Refer to the Excel display below and answer the given questions.Construct the multiple regression equation that expresses earthquake magnitude in terms of latitude, longitude, and depth.
Refer to the weights of garbage in Data Set 1 of Appendix B. Let the dependent variable be HHSIZE (household size), and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the weights of garbage in Data Set 1 of Appendix B. Let the dependent variable be HHSIZE (household size), and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the weights of garbage in Data Set 1 of Appendix B. Let the dependent variable be HHSIZE (household size), and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the weights of garbage in Data Set 1 of Appendix B. Let the dependent variable be HHSIZE (household size), and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the weights of garbage in Data Set 1 of Appendix B. Let the dependent variable be HHSIZE (household size), and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the weights of garbage in Data Set 1 of Appendix B. Let the dependent variable be HHSIZE (household size), and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to Data Set 5 in Appendix B and find the best multiple regression equation with number of Senate sittings as the dependent variable. (Don't include the number of each Parliament as an independent variable.) Is this equation suitable for predicting the number of Senate sittings in a given
In some cases, the best-fitting multiple regression equation is of the form Å· = bQ + bQ + b-,x2. The graph of such an equation is a parabola. Using the data set listed in the margin, let xx = x, and, creating an x2 row, let x2 = x2. Find the multiple regression equation for the
Refer to the Excel display below and answer the given questions.Identifya. The P-value corresponding to the overall significance of the multiple regression equation.b. The value of the multiple coefficient of determination R2.c. The adjusted value of R1.
Seismic activity has been detected as 48.2°N latitude and 124.99°W longitude, at a depth of 1 m.a. Find the predicted magnitude of the earthquake.b. The seismic activity in question actually had a magnitude of 0.9 ML. How accurate is the predicted weight from part (a)?
Refer to the temperature and precipitation data in Data Set 4 of Appendix B. Let the dependent variable be AVTEMP, and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the temperature and precipitation data in Data Set 4 of Appendix B. Let the dependent variable be AVTEMP, and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the temperature and precipitation data in Data Set 4 of Appendix B. Let the dependent variable be AVTEMP, and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the temperature and precipitation data in Data Set 4 of Appendix B. Let the dependent variable be AVTEMP, and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Refer to the weights of garbage in Data Set 1 of Appendix B. Let the dependent variable be HHSIZE (household size), and let the independent variables be those given in the exercise. (The data sets are already stored on the data disk and STATDISK.) Use software such as Excel, Minitab, or STATDISK to
Use the data in the accompanying table. The data come from a study of ice cream consumption that spanned the springs and summers of three years. The ice cream consumption is in liters per capita per week, price of the ice cream is in dollars, family income of consumers is in dollars per week, and
Use the data in the accompanying table. The data come from a study of ice cream consumption that spanned the springs and summers of three years. The ice cream consumption is in liters per capita per week, price of the ice cream is in dollars, family income of consumers is in dollars per week, and
Use the data in the accompanying table. The data come from a study of ice cream consumption that spanned the springs and summers of three years. The ice cream consumption is in liters per capita per week, price of the ice cream is in dollars, family income of consumers is in dollars per week, and
Use software such as Excel, Minitab, or STATDISK to find the multiple regression equation of the form = bQ + blxl + b2x2 + b3x3, where the dependent variable y represents consumption, x, represents price, x-, represents income, and x3 represents temperature. Also identify the value of the multiple
Use the sample data in the accompanying table. The table includes the results for the top performers in the 1996 Molson Indy Toronto. Note that the data in the Final Position column are ordinal and thus should not be used in the regressions. The distance between the first and second final
Use the sample data in the accompanying table. The table includes the results for the top performers in the 1996 Molson Indy Toronto. Note that the data in the Final Position column are ordinal and thus should not be used in the regressions. The distance between the first and second final
Use the sample data in the accompanying table. The table includes the results for the top performers in the 1996 Molson Indy Toronto. Note that the data in the Final Position column are ordinal and thus should not be used in the regressions. The distance between the first and second final
Use the sample data in the accompanying table. The table includes the results for the top performers in the 1996 Molson Indy Toronto. Note that the data in the Final Position column are ordinal and thus should not be used in the regressions. The distance between the first and second final
In 1970, the mean time between eruptions of the Old Faithful geyser was 66 minutes. Refer to the intervals (in minutes) between eruptions for the more recent data listed in Data Set 16 of Appendix B.a. Test the claim of Yellowstone National Park geologist Rick Hutchinson that eruptions now occur at
The Marc Michael Advertising Company has prepared two different television commercials for Taylor's women's jeans. One commercial is humorous and the other is serious. A test screening involves a standard scale with higher scores indicating more favourable responses. The results are listed here.
In studying the effects of heredity and environment on intelligence, it has been helpful to analyze IQs of identical twins who were separated soon after birth.Identical twins share identical genes inherited from the same fertilized egg. By studying identical twins raised apart, we can eliminate the
Do strong El Nino phenomena increase temperatures during springtime? Using the data in the following table, test the claim that the progression of a strong El Nino, from the spring of onset to the next spring, has no effect on Canadian temperature departures from seasonal norms. Use a 0.05 level of
The Life Trust Insurance Company funded a university study of drinking and driving. After 30 randomly selected drivers were tested for reaction times, they were given two drinks and tested again, with the result that 22 had slower reaction times, 6 had faster reaction times, and 2 received the same
Mental measurements of young children are often made by giving them blocks and telling them to build a tower as tall as possible. One experiment of block building was repeated a month later, with the times (in seconds) listed below. Use a 0.01 level of significance to test the claim that there is
Refer to the number of Senate sittings for Parliaments in Data Set 5 of Appendix B. Use the data for Parliaments of at least three years' duration. Assuming past Parliaments are representative of Parliaments in general, test the claim that the median number of Senate sittings for Parliaments of at
A sample of 10 randomly selected IQ scores is obtained from the population of professional athletes. We want to test the claim that the population is centered at the IQ score of 100. a. Is it possible to have sample data such that the sign test leads to rejection of the null hypothesis that the
In the sign test procedure described in this section, we excluded ties (represented by 0 instead of a sign of + or -). A second approach is to treat half of the 0s as positive signs and half as negative signs. (If the number of 0s is odd, exclude one so that they can be divided equally.) With a
Table A-7 lists critical values for limited choices of a. Use Table A-l to add a new column in Table A-7 (down to n = 15) that represents a significance level of 0.03 in one tail or 0.06 in two tails. For any particular n we use p = 0.5, as the sign test requires the assumption that P(positive
An environmental study compared the use of motorized vehicles in different countries over time. The accompanying table shows comparative data (in billions of vehicle-kilometres driven) for two countries in selected years. Use a 0.025 significance level to test the claim that there are more
The Alumni Association of the University of British Columbia tries to track the whereabouts and careers of UBC graduates. In a sample of 88 graduates known to be living outside of Canada, 51 are living in the United States. At the 0.05 significance level, test the claim that most (more than half)
A college aptitude test was given to 100 randomly selected high-school seniors. After a period of intensive training, a similar test was given to the same students: 59 students received higher grades, 36 received lower grades, and 5 received the same grades. At the 0.05 level of significance, test
The Joliette Manufacturing Company claims that hiring is done without any gender bias. If 18 of the last 25 new employees are women, and job applicants are about half men and half women who are all qualified, is there sufficient evidence to charge gender bias? Use a 0.01 level of significance,
Refer to Data Set 16 in Appendix B. Test the claim that the intervals between eruptions of the Old Faithful geyser have a median greater than 77 min, which was the median about 20 years ago.
Using the weights of only the brown M&Ms listed in Data Set 11 of Appendix B, test the claim that the median is greater than 0.9085 g. (For the 1498 M&Ms to produce a total package weight of 1361 g, the mean weight must be at least 0.9085 g.) Use a 0.05 significance level. Based on the result, does
Refer to Data Set 6 in Appendix B. Use the paired data consisting of the return on invested capital (%) and return on equity (%) for the top 50 companies. If either value is not available (n.a.) for a company, omit that company from the analysis. Using a 0.05 level of significance, test the claim

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