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Homework answers / question archive / This data reflects student enrollment at a college in Southern California

This data reflects student enrollment at a college in Southern California

Statistics

This data reflects student enrollment at a college in Southern California.

  Traditional math pathway    Accelerated math pathway    Row totals    Female    1244    116    1360    Male    1054    54    1108    Column totals    2298    170    2468  

We want to determine if the probability that a student enrolls in a traditional math pathway is independent of gender. Which of the following pairs of probabilities is NOT a useful comparison?

  • 1054/2468 and 2298/2468
  • 1360/2468 and 1244/2298
  • 1108/2468 and 1054/2298
  • 2298/2468 1054/1108

 

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Answer:

The pair of probabilities that is NOT a useful comparison is:

1054/2468 and 2298/2468

Step-by-step explanation

These are my suggestions.

Note that, by definition, two events A and B are independent if :

?p(A/B)=p(A)?

In our case, consider the events:

?F:? select a female

?M:? select a male

?A:? the student enrolled in accelerated mathematics

?T:? the student enrolled in traditional mathematics

We have the following cases:

a) ?p(T/M)? and ?p(T)?

Where:

?p(T/M)=11081054?? and ?p(T)=24682298??

b)?p(M/T)? and ?p(M)?

Where:

?p(M/T)=22981244?? and ?p(M)=24681108??

c) ?p(F/T)? and ?p(F)?

Where:

?p(F/T)=22981244?? and ?p(F)=24681360??

d) ?p(T/F)? and ?p(T)?

Where:

?p(T/F)=13601244?? and ?p(T)=24682298??

Therefore, the pair of probabilities that is NOT a useful comparison is:

1054/2468 and 2298/2468

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