Two different professors teach an introductory statistics class at a local colle
ID: 3152891 • Letter: T
Question
Two different professors teach an introductory statistics class at a local college. The table below shows the distribution of final grades they reported. We wonder if one of the professors is an “easier” grader.
What is the correct type of test to use for this situation?
What are the conditions required to use this test? Have the conditions been satisfied? Explain.
State the null and alternative hypothesis.
What is the X^2 statistic and p-value for the test?
At the ? = .05 level, what conclusion can you draw about the two professors?
Explanation / Answer
The correct type of test is Chi-square test for independence.
Assumptions: Counted data collection: Count sof individual categories. Independence assumption: students obtianing grades in one category are indepdendent of each other. Randomization condition: This is an experiment, so data are randomized. 10% condition: The total number of students obtaining grades are less than 10% of all those obtaining grades under two categories. Exected cell frequency condition: The expected cell frequency meet the condition of at least 5.
H0: Professor Jones and Professor Smith are independent graders.
H1: Professor Jones and Professor Smith are not independent graders.
The Chi-square test statistic:
X^2=Summation (Obs-Exp)^2/Exp=(3-6.585)^2/6.585+...=7.225
The p value:0.117
The p value is not less than 0.05. Therefore, fail to reject null hypothesis. There is not sufficient sample evidence to conclude that Professor Jones and Professor Smith are not independent graders.
Observed Expected 3 6.585 11 12.622 14 12.073 9 7.134 8 6.585 9 5.415 12 10.378 8 9.927 4 5.866 4 5.415Related Questions
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