Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 10–1 Scatter Plots and Correlation 549c. State the hypotheses.d. Test the significance of the correlation coefficient ata 0.05, using Table I.e. Give a brief explanation of the type of relationship.12. Gas Tax and Fuel Use The data below indicatethe state gas tax in cents per gallon and the fuel use perregistered vehicle (in gallons). Is there a significantrelationship between these two variables?Tax 21.5 23 18 24.5 26.4 19Usage 1062 631 920 686 736 684(The information in this exercise will be used forExercise 12 in Section 10–2.)Source: World Almanac.13. Commercial Movie Releases The yearlydata have been published showing the number ofreleases for each of the commercial movie studiosand the gross receipts for those studios thus far. Basedon these data, can it be concluded that there is arelationship between the number of releases and thegross receipts?No. of releases x 361 270 306 22 35 10 8 12 21Gross receipts y(million $) 3844 1962 1371 1064 334 241 188 154 125(The information in this exercise will be used forExercises 13 and 36 in Section 10–2 and Exercises 15and 19 in Section 10–3.)Source: www.showbizdata.com14. Forest Fires and Acres Burned Anenvironmentalist wants to determine the relationshipsbetween the numbers (in thousands) of forest fires overthe year and the number (in hundred thousands) of acresburned. The data for 8 recent years are shown. Describethe relationship.Number of fires x 72 69 58 47 84 62 57 45Number ofacres burned y 62 42 19 26 51 15 30 15Source: National Interagency Fire Center.(The information in this exercise will be used forExercise 14 in Section 10–2 and Exercises 16 and 20 inSection 10–3.)15. Alumni Contributions The director of analumni association for a small college wants todetermine whether there is any type of relationshipbetween the amount of an alumnus’s contribution(in dollars) and the years the alumnus has beenout of school. The data follow. (The information is usedfor Exercises 15, 36, and 37 in Section 10–2 andExercises 17 and 21 in Section 10–3.)Years x 1 5 3 10 7 6Contribution y 500 100 300 50 75 8016. State Debt and Per Capita Tax An economicsstudent wishes to see if there is a relationship betweenthe amount of state debt per capita and the amount oftax per capita at the state level. Based on the followingdata, can she or he conclude that per capita state debtand per capita state taxes are related? Both amounts arein dollars and represent five randomly selected states.(The information in this exercise will be used forExercises 16 and 37 in Section 10–2 and Exercises 18and 22 in Section 10–3.)Per capita debt x 1924 907 1445 1608 661Per capita tax y 1685 1838 1734 1842 1317Source: World Almanac.17. School Districts and Secondary Schools Arandom sample of states yielded the followingnumbers of local school districts and the correspondingnumbers of secondary schools. Is there a significantrelationship between the data?School districts 53 19 24 17 95 68Secondary schools 50 27 187 84 143 216Source: World Almanac.(The information in this exercise will be used forExercise 17 of Section 10–2.)18. Triples and Home Runs The data below showthe number of three-base hits (triples) and the numberof home runs hit during the season by a random sampleof MLB teams. Is there a significant relationshipbetween the data?Triples 25 23 51 19 20 43Home runs 212 199 144 160 149 122Source: New York Times Almanac.(The information in this exercise will be used forExercises 18 and 38 in Section 10–2.)19. Egg Production Recent agricultural datashowed the number of eggs produced and theprice received per dozen for a given year. Based onthe following data for a random selection of states,can it be concluded that a relationship existsbetween the number of eggs produced and the priceper dozen? (The information in this exercise will beused for Exercise 19 in Section 10–2.)No. of eggs(millions) x 957 1332 1163 1865 119 273Price per dozen(dollars) y 0.770 0.697 0.617 0.652 1.080 1.420Source: World Almanac.10–17