17. analyzing two - way tables you survey 83 college students and find that 65 live on campus, 31 have a car…

17. analyzing two - way tables you survey 83 college students and find that 65 live on campus, 31 have a car while at college, and 3 live off campus and do not have a car. is there an association between living on campus and having a car at college? explain. (see example 4.) 18. analyzing two - way tables the two - way table shows the results of a survey that asked students whether they will participate in a fundraiser. is there an association between class and participation? participate in fundraiser yes no freshman 47 15 sophomore 53 28 junior 45 30 senior 46 37 19. analyzing two - way tables refer to exercise 7. is there an association between gender and rating? explain. 20. analyzing two - way tables the two - way table shows the results of a survey that asked adults whether they participate in recreational skiing. is there an association between age and recreational skiing? is there a causal relationship between age and participating in recreational skiing? explain. age 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 ski yes 87 93 68 37 20 no 165 195 148 117 125

17. analyzing two - way tables you survey 83 college students and find that 65 live on campus, 31 have a car while at college, and 3 live off campus and do not have a car. is there an association between living on campus and having a car at college? explain. (see example 4.) 18. analyzing two - way tables the two - way table shows the results of a survey that asked students whether they will participate in a fundraiser. is there an association between class and participation? participate in fundraiser yes no freshman 47 15 sophomore 53 28 junior 45 30 senior 46 37 19. analyzing two - way tables refer to exercise 7. is there an association between gender and rating? explain. 20. analyzing two - way tables the two - way table shows the results of a survey that asked adults whether they participate in recreational skiing. is there an association between age and recreational skiing? is there a causal relationship between age and participating in recreational skiing? explain. age 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 ski yes 87 93 68 37 20 no 165 195 148 117 125

Answer

Explanation:

Step1: Calculate row - totals and column - totals for each table

For problem 17: Total number of students = 83. Number of students living on - campus = 65, number of students living off - campus = 83 - 65=18. Number of students with a car = 31, number of students without a car = 83 - 31 = 52. For problem 18: Row - totals for Freshman: 47 + 15=62, Sophomore: 53 + 28 = 81, Junior: 45+30 = 75, Senior: 46 + 37=83. Column - totals for Yes: 47+53 + 45+46 = 191, for No: 15 + 28+30 + 37 = 110. For problem 20: Row - totals for Yes: 87+93 + 68+37 + 20=305, for No: 165+195 + 148+117 + 125 = 750. Column - totals for 21 - 30: 87+165 = 252, 31 - 40: 93+195 = 288, 41 - 50: 68+148 = 216, 51 - 60: 37+117 = 154, 61 - 70: 20+125 = 145.

Step2: Calculate conditional probabilities

For problem 17: Let (A) be the event of living on - campus and (B) be the event of having a car. The probability of having a car given living on - campus (P(B|A)=\frac{\text{Number of on - campus students with a car}}{\text{Number of on - campus students}}). We know that the number of on - campus students is 65. Let's assume the number of on - campus students with a car is (x). We can find (x) from the information. The number of off - campus students without a car is 3. The number of students with a car is 31. Let the number of on - campus students with a car be (x), then the number of off - campus students with a car is (31 - x). The number of off - campus students is (83 - 65 = 18). So the number of off - campus students with a car is (18 - 3=15), and (x = 31 - 15 = 16). Then (P(B|A)=\frac{16}{65}\approx0.246). The probability of having a car (P(B)=\frac{31}{83}\approx0.373). Since (P(B|A)\neq P(B)), there is an association. For problem 18: For Freshman, the probability of participating (P(P|F)=\frac{47}{62}\approx0.758). For all students, the probability of participating (P(P)=\frac{191}{191 + 110}=\frac{191}{301}\approx0.635). Since (P(P|F)\neq P(P)), there is an association between class and participation. For problem 20: For the 21 - 30 age group, the probability of skiing (P(S|21 - 30)=\frac{87}{252}\approx0.345). For all ages, the probability of skiing (P(S)=\frac{305}{305 + 750}=\frac{305}{1055}\approx0.29). Since (P(S|21 - 30)\neq P(S)), there is an association between age and recreational skiing. A causal relationship is hard to determine just from the table. There could be other factors like physical ability, personal interest, etc. that influence skiing participation, not just age.

Answer:

  1. There is an association between living on campus and having a car.
  2. There is an association between class and participation.
  3. There is an association between age and recreational skiing. There is no clear causal relationship between age and participating in recreational skiing.