You having two employees working on commission - employee A and employee B. Over the course of 80 weeks, you observe the sales of each employee. Let X = the number of times employee A has more sales than employee B. You build the following line of reasoning:
Steps
1) You assume each sales observation is an independent, random outcome.
2) You assume each employee has equal likelihood of have greater sales in a week.
3) Using your statistics book, you conclude that X is distributed binomial with mean 40 and variance 20.
4) Based on this distribution, you conclude that you would observe X < 32 or X > 48 approximately 5% of the time.
5) You observe X = 53 and conclude that the probability that X < 32 or X > 48 is not 5%.
6) Because the probability that X < 32 or X > 48 is not 5%, you conclude employee A and employee B do not have equal likelihood of having greater sales in a week.
Which of these steps is part of deductive reasoning?

Question

Quizplus · Accepted Answer

Steps 1-4 use deductive reasoning to draw a conclusion based on the assumptions and the binomial distribution. Step 6 also uses deductive reasoning to reach a conclusion based on the observed probability not matching the expected probability. Step 5, however, is based on the observation of a specific outcome and is not deductive reasoning, but rather inductive reasoning.

You Having Two Employees Working on Commission - Employee a and Employee