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% |
…………………………………………………….
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.
…………………………………………………….
Hope this helps!
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