The table to the right shows counts of the number of days that employees were absent from a small manufacturing center. The null hypothesis is that the counts are uniformly distributed over the days of the week. (a) Find the degrees of freedom of χ2. (b) Find the expected number of absences on a Wednesday, if H0 holds. (c) Find the value of χ2 for testing H0.
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!
|
Days
|
|
|
|---|---|---|
|
Monday
|
24
|
|
|
Tuesday
|
54
|
|
|
Wednesday
|
42
|
|
|
Thursday
|
30
|
|
|
Friday
|
30
|
|
|
|
|
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To test the hypothesis is that the counts are uniformly distributed over the days of the week at 5% significance level.
The null and alternative hypothesis is,
The null hypothesis is that the counts are uniformly distributed over the days of the week.
the alternative hypothesis is that the counts are not uniformly distributed over the days of the week.
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