Please use the formulas and long hand, not in a computer basic stats class. 5. A
ID: 3152951 • Letter: P
Question
Please use the formulas and long hand, not in a computer basic stats class.
5. At a school pep rally, a group of sophomore students organized a free rafe 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 shy that sophomores organized the rafe and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. a. What are the expected frequencies of winners from each class? b. Conduct a signicance 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?
Explanation / Answer
A)
The expected frequencies are
36*0.30 = 10.8
36*0.25 = 9
36*0.25 = 9
36*0.20 = 7.2 [ANSWER]
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b)
Doing an observed/expected value table,
O E (O - E)^2/E
6 10.8 2.133333333
14 9 2.777777778
9 9 0
7 7.2 0.005555556
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 4.916666667 [ANSWER, CHI SQUARED TEST STATISTIC]
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As df = a - 1,
a = 4
df = a - 1 = 3
Thus, the p value is
p = 0.178001915 [ANSWER, P VALUE]
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c.
As P > 0.05, we fail to reject the original distribution.
There is no significant evidence that the results are not random. [CONCLUSION]