[5pts] A professor in the Sociology department would like to determine whether t

Question

[5pts] A professor in the Sociology department would like to determine whether there has been a significant change in grading practices over the years. It is known that the overall grade distribution for SOC316: Sociological Theory in 1985 had 14% As, 26% Bs, 31%Cs, 19% Ds, and 10% Fs. A sample of n = 200 sociology students who took this course over during the last year produced the following grade distribution:

A

B

C

D

E

32

61

64

31

12

Using an alpha level of .05, answer the following questions:

What is the null hypothesis? Write out the hypothesis in sentence form AND fill out the boxes:

A

B

C

D

E

%

%

%

%

%

What is the alternative hypothesis? Write out the hypothesis in sentence form.

What is the df for this chi-square test?

What is the critical value for this test?

Determine the expected frequency for each letter grade:

A

B

C

D

E

What is the value of the 2 statistic?

What decision about the null hypothesis does your test lead you to?

Interpret the findings from your chi-square test in sentence-form.

A

B

C

D

E

32

61

64

31

12

Explanation / Answer

H0: No difference in grade distribution between 1985 and last semester
H1: There is a difference in grade distribution between 1985 and last semester

O - Observed frequencies
E - Expected frequencies

----O ----- E
A - 32 (200)*(0.14) = 28
B - 61 (200)*(0.26) = 52
C - 64 (200)*(0.31) = 62
D - 31 (200)*(0.19) = 38
F - 12 (200)*(0.10) = 20

Chi-squared = [ O(i)-E(i) )^2 / E(i)

Chi-square = (32-28)^2/28+(61-52)^2/52+(64-62)^2/62+(... = 6.6831

The critical chi-squared with 5-1= 4 degrees of freedom
(assuming 5% level of significance) is 11.07
Calculated chi-squared is smaller than the critical chi-square so we fail to reject the null hypothesis. We conclude that the data do not indicate a change in the grade distribution

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