Determine if the statements below are true or false. For each false statement, suggest an alternative wording to make it a true statement. (a) As the degrees of freedom increases, the mean of the chi-square distribution increases. (b) If you found χ 2 = 10 with df = 5 you would fail to reject H0 at the 5% significance level. (c) When finding the p-value of a chi-square test, we always shade the tail areas in both tails. (d) As the degrees of freedom increases, the variability of the chi-square distribution decreases
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!
. Determine if the statements below are true or false. For each false statement,
suggest an alternative wording to make it a true statement.
(a) As the degrees of freedom increases, the mean of the chi-square distribution increases.
(b) If you found χ
2 = 10 with df = 5 you would fail to reject H0 at the 5% significance level.
(c) When finding the p-value of a chi-square test, we always shade the tail areas in both tails.
(d) As the degrees of freedom increases, the variability of the chi-square distribution decreases
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