Concept explainers
Testing for a
25. 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?
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ESSENTIALS OF STATISTICS 6TH ED W/MYSTA
- 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_forwardInterpreting a Computer Display. In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the StatCrunch display and answer the given questions or identify the indicated items. The display is based on Data Set 5 “Family Heights” in Appendix B. Height of Son A son will be bom to a father who is 70 in. tall and a mother who is 60 in. tall. Use the multiple regression equation to predict the height of the son. Is the result likely to be a good predicted value? Why or why not?arrow_forwardA study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Number ofFacilities AverageDistance(miles) 9 1.65 11 1.11 16 0.83 21 0.62 27 0.51 30 0.48 (a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. A scatter diagram has 6 points. The horizontal axis ranges from 0 to 1.8 and is labeled: Distance. The vertical axis ranges from 5 to 35 and is labeled: Number. Moving from left to right, the leftmost point is at approximately (0.48, 30), with the next five points extending downward. The points decrease steeply at first and then level off. A scatter diagram has 6 points. The horizontal axis ranges from 5 to 35 and is labeled: Number. The vertical axis ranges from 0 to 1.8 and is labeled: Distance. Moving from left to right, the leftmost point is at…arrow_forward
- A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Number ofFacilities AverageDistance(miles) 9 1.65 11 1.11 16 0.83 21 0.62 27 0.51 30 0.48 (a) Develop a scatter diagram for these data, treating average distance traveled as the dependent variable. A scatter diagram has 6 points. The horizontal axis ranges from 0 to 1.8 and is labeled: Distance. The vertical axis ranges from 5 to 35 and is labeled: Number. Moving from left to right, the leftmost point is at approximately (0.48, 30), with the next five points extending downward. The points decrease steeply at first and then level off. A scatter diagram has 6 points. The horizontal axis ranges from 5 to 35 and is labeled: Number. The vertical axis ranges from 0 to 1.8 and is labeled: Distance. Moving from left to right, the leftmost point is at…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_forwardUse the table below to answer the following questions: (a) Find the value of the linear correlation coefficient. (b) Assuming a 0.01 significance level, find the critical values. (c) Is there sufficient evidence to support the claim of a linear correlation? Explain your reasoningarrow_forward
- Use table of critical values for correlation coefficient.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_forwarddata set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of α=0.05. Click here to view a table of critical values for the correlation coefficient. LOADING... Correlation matrix: Variables Paper Glass Paper 1 0.4325 Glass 0.4325 1 Determine the null and alternative hypotheses. Identify the test statistic, r. r= (Round to three decimal places as needed.) Identify the critical value(s). (Round to three decimal places as needed.) A.There are two critical values at r=± ______ B.There is one critical value at r= _____ State the conclusion. Because the absolute value of the test statistic is ▼ greater than or…arrow_forward
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