How do you differentiate the probability distributions?
A probability distribution may be either discrete or continuous. A discrete distribution means that X can assume one of a countable (usually finite) number of values, while a continuous distribution means that X can assume one of an infinite (uncountable) number of different values.
How to compare two populations from independent populations?
As with comparing two population proportions, when we compare two population means from independent populations, the interest is in the difference of the two means. In other words, if μ 1 is the population mean from population 1 and μ 2 is the population mean from population 2, then the difference is μ 1 − μ 2.
Which is the best description of a probability distribution?
• Distribution of probability values (i.e. probability distributions) are best portrayed by the probability density function and the probability distribution function. • The probability distribution function can be represented as values in a table, but that is not possible for the probability density function because the variable is continuous.
When to use t-distribution to model difference in population mean?
The variable is normally distributed in both populations. If it is not known, samples of more than 30 will have a difference in sample means that can be modeled adequately by the T-distribution. As we discussed in “Hypothesis Test for a Population Mean,” T-procedures are robust even when the variable is not normally distributed in the population.
When is the sample mean difference statistically significant?
In practice, when the sample mean difference is statistically significant, our next step is often to calculate a confidence interval to estimate the size of the population mean difference. The confidence interval gives us a range of reasonable values for the difference in population means μ 1 − μ 2.