At a school pep rally a group of sophomore students organize

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 sophmores organized the raffle and also won the most prizes. Your school is comopsed of 30% freshmen, 25% sophmores, 25% juniors, and 20% 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?

Solution

(a)

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(b) The test hypothesis:

Null hypothesis: the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group.

Alternative hypothesis: the winners of the prizes were distributed throughout the classes as would not be expected based on the percentage of students in each group.