The following table summarizes the outcome for 70 people who attended a picnic, some of whom ate potato salad and some of whom became ill. Became ILL Yes No Total Salad-Yes 22 24 46 Salad-No 1 23 24 Total 23 47 70 Compute the odds ratio, . (Please Show All Work). Explain its meaning in context to the problem. If X is the probability that a person becomes ill given that he/she ate salad, use Fisher’s Exact Test to compute P(X 22). (Please Show All Work) Compute the exact probability using the Binomial Distribution NOT the Normal approximation. (This is basically the McNemar’s Test). (Please Show All Work)
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!
The following table summarizes the outcome for 70 people who attended a picnic, some of whom ate potato salad and some of whom became ill.
|
|
Became ILL |
|
|
|
|
Yes |
No |
Total |
|
Salad-Yes |
22 |
24 |
46 |
|
Salad-No |
1 |
23 |
24 |
|
Total |
23 |
47 |
70 |
- Compute the odds ratio, . (Please Show All Work). Explain its meaning in context to the problem.
- If X is the probability that a person becomes ill given that he/she ate salad, use Fisher’s Exact Test to compute P(X 22). (Please Show All Work)
- Compute the exact probability using the Binomial Distribution NOT the Normal approximation. (This is basically the McNemar’s Test). (Please Show All Work)
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