Concept explainers
Testing for a
27. Sports Diameters (cm), circumferences (cm), and volumes (cm3) from balls used in different sports are listed in the table below. Is there sufficient evidence to conclude that there is a linear correlation between diameters and circumferences? Does the scatterplot confirm a linear association?
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Elementary Statistics (13th Edition)
- Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of α = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.) Tips Listed below are amounts of bills for dinner and the amounts of the tips that were left. The data were collected by students of the author. Is there sufficient evidence to conclude that there is a linear correlation between the bill amounts and the tip amounts? If everyone were to tip with the same percentage, what should be the value of r?arrow_forwardTesting for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of α = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.) Revised mpg Ratings Listed below are combined city-highway fuel economy ratings (in mi/gal) for different cars. The old ratings are based on tests used before 2008 and the new ratings are based on tests that went into effect in 2008. Is there sufficient evidence to conclude that there is a linear correlation between the old ratings and the new ratings? What do the data suggest about the old ratings?arrow_forwardTesting for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of α = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.) Manatees Listed below are numbers of registered pleasure boats in Florida (tens of thousands) and the numbers of manatee fatalities from encounters with boats in Florida for each of several recent years. The values are from Data Set 10 “Manatee Deaths” in Appendix B. Is there sufficient evidence to conclude that there is a linear correlation between numbers of registered pleasure boats and numbers of manatee boat fatalities?arrow_forward
- Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of α = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.) POTUS Media periodically discuss the issue of heights of winning presidential candidates and heights of their main opponents. Listed below are those heights (cm) from several recent presidential elections (from Data Set 15 “Presidents” in Appendix B). Is there sufficient evidence to conclude that there is a linear correlation between heights of winning presidential candidates and heights of their main opponents? Should there be such a correlation?arrow_forwardNumber 16arrow_forwardconstruct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6 using α = 0.05 Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-3 exercises.) 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 °F (based on data from The Song of Insects by George W. Pierce, Harvard University Press). Is there sufficient evidence to conclude that there is a linear correlation between the number of chirps in 1 min and the temperature?arrow_forward
- The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y. Group of answer choices True Falsearrow_forwardSolve for the following: Expressed final answers in 4-decimal places. Compute for the coefficient of correlation coefficient and interpret its meaning.arrow_forwardKia assesses people's levels of gratitude and stress that occur naturally to determine if a relationship exists between the two variables. Kia is using a(n): a. quasi-experimental design b. experimental design c. descriptive design d. correlational designarrow_forward
- PART A. Solve for the Pearson Product-Moment Coefficient of Correlation. 24 43 34 76 54 87 90 Y 34 65 56 34 90 65 47arrow_forwardGive an example of a correlation study, and identify the independent and dependent variables.arrow_forwardCigarette Tar and Nicotine The table below lists measured amounts (mg) of tar, carbon monoxide (CO), and nicotine in king size cigarettes of different brands (from Data Set 13 “Cigarette Contents” in Appendix B). a. Is there is sufficient evidence to support a claim of a linear correlation between tar and nicotine? b. What percentage of the variation in nicotine can be explained by the linear correlation between nicotine and tar? c. Letting y represent the amount of nicotine and letting x represent the amount of tar, identify the regression equation. d. The Raleigh brand king size cigarette is not included in the table, and it has 23 mg of tar. What is the best predicted amount of nicotine? How does the predicted amount compare to the actual amount of 1.3 mg of nicotine?arrow_forward
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