Dr Myers Mr Murray and Mr Tremblay have always maintained th

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.

Solution

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.