A researcher is interested in the relationship between sport categories and self-esteem. A sample of n=9 people is obtained, all of whom exclusively participate in one of the sport activities on a weekly basis: soccer, volleyball, or tennis. Each person is given a self-esteem (0-15) test and the researcher also records the person’s sport activities. The self-esteem scores from this study are shown in the following table. Sport Soccer Volleyball Tennis 9 11 11 10 13 6 8 12 7 (10’) Based on these data, can the researcher conclude that there is a significant relationship between sport activity and self-esteem? Hand calculate the F- statistics and test at the 0.05 level of significance.
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 researcher is interested in the relationship between sport categories and self-esteem. A sample of n=9 people is obtained, all of whom exclusively participate in one of the sport activities on a weekly basis: soccer, volleyball, or tennis. Each person is given a self-esteem (0-15) test and the researcher also records the person’s sport activities. The self-esteem scores from this study are shown in the following table.
|
Sport |
||
|
Soccer |
Volleyball |
Tennis |
|
9 |
11 |
11 |
|
10 |
13 |
6 |
|
8 |
12 |
7 |
(10’) Based on these data, can the researcher conclude that there is a significant relationship between sport activity and self-esteem? Hand calculate the F- statistics and test at the 0.05 level of significance.
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