Chi Square

Question

At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize  winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. You school is composed of 30 percent freshman, 25 percent sophmores, 25 percent juniors, and 20 percent seniors 

 

 

a. What are the expected frequencies of winners from each class?

b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values. 

c. what do you conclude?

Answer 1

Hi Ashley,

         The expected frequencies are that which would be produces by a truly random drawing. So we would have

 

Freshmen   30% of 36 =11 (rounded to an integer)

Soph.         25% of 36=  9

Junior         25% of 36=  9

Senior         20% of 36=  7

 

         The actual or observed frequencies are;

Freshmen                        6

Soph                             14

Junior                              9

Senior                             7

 

It looks like the Sophmores might be taking advantage of the freshmen. If we pick a significance of 95% or alpha of .05 and H0 that the expected and actual are the same and run a Chitest I got p=.00362. So we reject H0. 

So we have to conclude that it is highly unlikely that this distribution would arise by chance.

 

Hope this is helpful

 

Jim