How to compare two populations in a statistic?
We arbitrarily label one population as Population 1 and the other as Population 2, and subscript the proportion of each population that possesses the characteristic with the number 1 or 2 to tell them apart. We draw a random sample from Population 1 and label the sample statistic it yields with the subscript 1.
Is the percentage of a population the same or different?
… Both percentages in the first cases are the same but a change of one person in each of the populations obviously changes percentages in a vastly different proportion. Should I take that into account when presenting the data?
How is a percentage related to a number?
A percentage is also a way to describe the relationship between two numbers. For example, we can say that 5 is 20% of 25, or 2 is 5% of 40. When we talk about a percentage, we can think of the % sign as meaning 1/100.
When to use pooled variance for Population 1?
When we have good reason to believe that the variance for population 1 is equal to that of population 2, we can estimate the common variance by pooling information from samples from population 1 and population 2. An informal check for this is to compare the ratio of the two sample standard deviations.
Is there a difference between two population parameters?
For example, μ 1 − μ 2 = 0 would mean that μ 1 = μ 2, and there would be no difference between the two population parameters. Similarly for two population proportions. Although we focus on the difference equalling zero, it is possible to test for specific values of the difference using the methods presented.
How to test for a difference in population proportions?
Test at a 1% level of significance. The problem asks for a difference in proportions, making it a test of two proportions. Let A and B be the subscripts for medication A and medication B, respectively. Then pA and pB are the desired population proportions.
Which is an example of comparing two proportions?
Additionally, most of our examples thus far have involved left tailed tests in which the alternative hypothesis involved H A: p < p 0 or right-tailed tests in which the alternative hypothesis involved H A: p > p 0. Here, let’s consider an example that tests the equality of two proportions against the alternative that they are not equal.