Exercise 3 At Anytown College, the administration would like the students, grade
ID: 3324860 • Letter: E
Question
Exercise 3 At Anytown College, the administration would like the students, grade distribution to be 25% AS, 30% B's, 25% C's, and 20% D's. The school's president thinks that the instructors may not be following this guideline, so he takes a random sample of grades to check his suspicion. A random sample of 30 grades yields 9 A's, 15 B's, 3 C's, and 3 D's. The president wishes to test H0 : PA = 0.25, PB 0.30, pc = 0.25, PD = 0.20 (a) Calculate the value of the apporpriate test statistic. (b) State the critical value for this test, and your statistical decision using a 5% significance level.Explanation / Answer
Here we use the goodness of fit test.
The Hypothesis:
H0: There is no difference between the observed and expected frequencies, i.e The instructors are following the guidelines.
Ha: There is a difference in observed and expected frequencies, that is the instructors are not following the guidelines.
(a) The Test statistic: The below table show the calculation of the test Statistic.
2test = 8.5
(b) The Critical Value: The 2 critical at = 0.05, df = n -1 = 4 - 1 = 3 is 7.814
The p Value: The p value at 2test = 3.78 , df = 3 is
p value = 0.0367
The Decision Rule: If 2test is > 2 Critical, Then Reject H0
Also, If p value is < , then Reject H0.
The Decision: Since 2test(8.5) is > 2 Critical(7.814), We Reject H0
Since If p value (0.0367) is < (0.05), We Reject H0.
The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the instructors are not following the guidelines.
Observed Expected Expected (O-E)2 (O-E)2/E A 9 0.25 7.5 2.25 0.3 B 15 0.3 9 36 4 C 3 0.25 7.5 20.25 2.7 D 3 0.2 6 9 1.5 Total 30 1 30 67.5 8.5Related Questions
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