randomly selected seniors and freshmen from four different schools were surveyed as to whether they…

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.\na.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|38|10|48|\n|freshmen|16|34|50|\n|total|54|44|98|\nb.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|11|41|52|\n|freshmen|35|15|50|\n|total|46|56|102|\nc.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|26|18|44|\n|freshmen|39|27|66|\n|total|65|45|110|\nd.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|40|60|100|\n|freshmen|30|45|75|\n|total|70|105|175|

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.\na.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|38|10|48|\n|freshmen|16|34|50|\n|total|54|44|98|\nb.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|11|41|52|\n|freshmen|35|15|50|\n|total|46|56|102|\nc.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|26|18|44|\n|freshmen|39|27|66|\n|total|65|45|110|\nd.\n| |baseball|football|total|\n|--|--|--|--|\n|seniors|40|60|100|\n|freshmen|30|45|75|\n|total|70|105|175|

Answer

Explanation:

Step1: Calculate row - column proportions

For a two - way table to show no association, the proportion of students who prefer baseball among seniors should be approximately equal to the proportion of students who prefer baseball among freshmen. For each table, calculate the proportion of baseball - preferring students for seniors ($p_{s}$) and freshmen ($p_{f}$). The formula for proportion is $p=\frac{\text{Number of baseball - preferring students}}{\text{Total number of students in the group}}$.

Step2: Analyze Table A

For seniors in School 1, $p_{s}=\frac{38}{48}\approx0.792$. For freshmen in School 1, $p_{f}=\frac{16}{50} = 0.32$. Since $0.792\neq0.32$, there is an association.

Step3: Analyze Table B

For seniors in School 2, $p_{s}=\frac{11}{52}\approx0.212$. For freshmen in School 2, $p_{f}=\frac{35}{50}=0.7$. Since $0.212\neq0.7$, there is an association.

Step4: Analyze Table C

For seniors in School 3, $p_{s}=\frac{26}{44}\approx0.591$. For freshmen in School 3, $p_{f}=\frac{39}{66}=0.591$. Since $p_{s}\approx p_{f}$, there is no association.

Step5: Analyze Table D

For seniors in School 4, $p_{s}=\frac{40}{100} = 0.4$. For freshmen in School 4, $p_{f}=\frac{30}{75}=0.4$. Since $p_{s}=p_{f}$, there is no association.

Answer:

C. School 3, D. School 4