At large universities, students in statistics courses are often taught by teachi

Question

At large universities, students in statistics courses are often taught by teaching assistants (TAs) and one section is taught by the course supervisor who is a senior professor. The distribution of grades for the hundreds of students taught by TAs last semester was 32% A, 41% B, 20% C, and 7% D/F. The grades assigned by the senior professor to students in his section were 22 As, 38 Bs, 20 Cs, and 11 D/Fs. You plan to do a chi-square goodness of fit test to see if the senior professor's grades follow a different distribution. How many degrees of freedom are there?

a) 1 b) 2 c) 3 d) 4

What is the value of the chi-square statistic?

a) 3.00 b) 0.91 c) 5.30 d) 6.46

What is the P-value of your test?

a) 0.0457 b) 0.1513 c) 0.1826 d) 0.3652

Explanation / Answer

applying goodness of fit test on above:

degree of freedom =number of categories-1 =4-1=3 option C

value of chi-square statistic =5.30 option C

p value =0.1513 option B

please revert for any clarification required

observed Expected Chi square grade Probability O E=total*p =(O-E)^2/E A 0.320 22.000 29.12 1.74 B 0.410 38.000 37.31 0.01 C 0.200 20.000 18.20 0.18 D 0.070 11.000 6.37 3.37 1 91 91 5.2970

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