A teacher hypothesizes that th
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 BC D F 6 14 22 8 4 Considering the statement above, what are theexpected frequencies for grades A and F respectively?
Answer:
Given, N = 54.
Now, we can tabulate the expected percentages from the nullhypothesis as follows:
Grade | ExpectedPercentage |
A | 10% |
B | 23% |
C | 45% |
D | 14% |
F | 8% |
Total | 100% |
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Calculations:
To find the respective expected frequencies, we can apply thefollowing formula:
Expected Frequency(fe) = N x (Expected percentage from nullhypothesis)
Uaing the above formula, the expected frequencies(fe) can be tabulated as follows:
Grade | ExpectedPercentage | 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 5.40and 4.32 respectively.
…………………………………………………….
Further inference:
Here, since we are given the observed frequencies(fo) as well, we can tabulate andcompare the values of feandfo for a check on the reliability ofthe 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 lievery close to each other, which implies that the stated hypothesisis successful for the prediction of approximate grade frequenciesbeforehand.
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Hope this helps!
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