Question

A teacher hypothesizes that the final grades in her class (N = 54) are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. At the end of the semester, she has the following grades: A B C D F 6 14 22 8 4 Considering the statement above, what are the expected frequencies for grades A and F respectively?

Answer 1

Given, N = 54.

Now, we can tabulate the expected percentages from the null hypothesis as follows:

Grade	Expected Percentage
A	10%
B	23%
C	45%
D	14%
F	8%
Total	100%

.............................................................

Calculations:

To find the respective expected frequencies, we can apply the following formula:

Expected Frequency (f_e) = N x (Expected percentage from null hypothesis)

Uaing the above formula, the expected frequencies (f_e) can be tabulated as follows:

Grade	Expected Percentage	Expected Frequency (fe)
A	10%	54 x 0.1 = 5.40
B	23%	54 x 0.23 = 12.42
C	45%	54 x 0.45 = 24.30
D	14%	54 x 0.14 = 7.56
F	8%	54 x 0.08 = 4.32
Total	100%	54.0

.............................................................

Result:
Hence, the expected frequencies for grades A and F are 5.40 and 4.32 respectively.

.............................................................

Further inference:

Here, since we are given the observed frequencies (f_o) as well, we can tabulate and compare the values of f_eand f_o for a check on the reliability of the null hypothesis:

-	A	B	C	D	F	Total
Observed Frequency (fo)	6	14	22	8	4	54.0
Expected Frequency (fe)	5.40	12.42	24.30	7.56	4.32	54.0

From the table, it is evident that the observed and expected lie very close to each other, which implies that the stated hypothesis is successful for the prediction of approximate grade frequencies beforehand.

.............................................................

Hope this helps!