A professor states papers are graded using the following categories: excellent, above average, average, and below average. Furthermore, the professor maintains that turned-in papers are graded graciously and offers the following distribution of percentages as an estimate of the manner in which the grades are distributed. Excellent Above Average Average Below Average 25% 35% 25% 15% A group of students suspects the professor may indeed be generous but only in the perception of being an easy grader. All of the students who had previously taken this professor’s course in the last three years are available, and amazingly, they still have their papers. A random sample of 100 former students is taken, and the actual distribution of evaluations is recorded. Excellent Above Average Average Below Average 25% 35% 25% 15% O= 20 O= 25 O= 30 0= 25 Note that since the sample size is 100, the observed frequencies sum to 100. Is there a reason to conclude that the professor’s claim is mistaken? Find the Test statistics; if the alpha = 0.05
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A professor states papers are graded using the following categories: excellent, above average, average, and below average. Furthermore, the professor maintains that turned-in papers are graded graciously and offers the following distribution of percentages as an estimate of the manner in which the grades are distributed.
| Excellent | Above Average | Average | Below Average |
|---|---|---|---|
| 25% | 35% | 25% | 15% |
A group of students suspects the professor may indeed be generous but only in the perception of being an easy grader. All of the students who had previously taken this professor’s course in the last three years are available, and amazingly, they still have their papers. A random sample of 100 former students is taken, and the actual distribution of evaluations is recorded.
| Excellent | Above Average | Average | Below Average |
|---|---|---|---|
| 25% | 35% | 25% | 15% |
| O= 20 | O= 25 | O= 30 | 0= 25 |
Note that since the
Find the Test statistics; if the alpha = 0.05
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