Dr Myers, Mr. Murray and Mr. Tremblay have always maintained that they give the
ID: 3429393 • Letter: D
Question
Dr Myers, Mr. Murray and Mr. Tremblay have always maintained that they give the same proportion of A grades in their statistics courses. An enterprising student wishes to test this assertion and proceeds to take a random sample of former statistics students. The results are shown below:
Professor Dr. Myers Mr. Murray Mr. Tremblay
A Grades 30 24 16
Non A Grades 170 76 84
At an alpha level of 0.05 test the contention that the proportion of A grades are the same for the three professors.
Explanation / Answer
H0: Proportions are the same i.e. p1 =p2=p3 =0.0175
Ha: Atlease Proportions are different.
Two tailed chi square test
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Total A grades = 70
Total students = 400
Proportion combined = 0.175
Let us tabulate observed and expected frequencies in the table.
Row #CategoryObservedExpected chi square
Myers 30 35 50.000% 0.7142
Murray 24 17.5 25.000% 2.4143
Tremblay 16 17.5 25.000% 0.1285
Total 3.2570
P value and statistical significance:
Chi squared equals 3.257 with 2 degrees of freedom.
The two-tailed P value equals 0.1962
By conventional criteria, this difference is considered to be not statistically significant, as 0.1962>0.05 alpha level.
The P value answers this question: If the theory that generated the expected values were correct, what is the probability of observing such a large discrepancy (or larger) between observed and expected values? A small P value is evidence that the data are not sampled from the distribution you expected. But here our p value >0.05
Hence the proportion of A grades are the same for the three professors.
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