Question

randomly selected seniors and freshmen from four different schools were surveyed as to whether they preferred baseball or football. choose all of the tables that show no association between being a senior and preferring baseball.
a. school 1

	baseball	football	total
freshmen	16	34	50
total	54	44	98

b. school 2

	baseball	football	total
freshmen	35	15	50
total	46	56	102

c. school 3

	baseball	football	total
freshmen	39	27	66
total	65	45	110

d. school 4

	baseball	football	total
freshmen	30	45	75
total	70	105	175

Explanation:

Step1: Recall the concept of no - association

If there is no association between being a senior and preferring baseball, then the proportion of seniors who prefer baseball should be approximately equal to the proportion of freshmen who prefer baseball. That is, $\frac{\text{Number of senior baseball - lovers}}{\text{Total number of seniors}}\approx\frac{\text{Number of freshman baseball - lovers}}{\text{Total number of freshmen}}$.

Step2: Analyze Table A

For School 1: Proportion of seniors who prefer baseball is $\frac{38}{48}\approx0.792$. Proportion of freshmen who prefer baseball is $\frac{16}{50} = 0.32$. Since $0.792
eq0.32$, there is an association.

Step3: Analyze Table B

For School 2: Proportion of seniors who prefer baseball is $\frac{11}{52}\approx0.212$. Proportion of freshmen who prefer baseball is $\frac{35}{50}=0.7$. Since $0.212
eq0.7$, there is an association.

Step4: Analyze Table C

For School 3: Proportion of seniors who prefer baseball is $\frac{26}{44}\approx0.591$. Proportion of freshmen who prefer baseball is $\frac{39}{66}=0.591$. Since the two proportions are approximately equal, there is no association.

Step5: Analyze Table D

For School 4: Proportion of seniors who prefer baseball is $\frac{40}{100} = 0.4$. Proportion of freshmen who prefer baseball is $\frac{30}{75}=0.4$. Since the two proportions are equal, there is no association.

Answer:

C. School 3, D. School 4