a. Calculate the unbiased sample standard deviation b. Determine the critical value of the upper limit c. Determine the critical value of the lower limit d. The lower limit of the confidence interval is: Answer e. The upper limit of the confidence interval is: Answer 1. Interpretation: We are 99% confident that the calculated interval contains the population variance of the lengths of this species of fish. (Choose one answer) 1) Interpretation: 999% of the sample of mini-test 1 marks lies within the interval. 2) Interpretation: The population variance of the lengths of this species of fish will fall within the calculated confidence interval 99% of the time. 3) Interpretation: There is a 99% chance that the population variance of the lengths of this species of fish is in the calculated interval.
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!
| X | (X-xbar)^2 |
| 45 | 1.5625 |
| 58 | 138.0625 |
| 36 | 105.0625 |
| 42 | 18.0625 |
| 43 | 10.5625 |
| 41 | 27.5625 |
| 42 | 18.0625 |
| 63 | 280.5625 |
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