When testing the difference between two population proportions the test statistic is used?
A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions. The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same.
What assumptions are necessary to perform a large sample test for the difference between two populations means?
The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size, and equality of variance in standard deviation.
How to compare two populations by mean and standard deviation?
Each population has a mean and a standard deviation. We arbitrarily label one population as Population 1 and the other as Population 2, and subscript the parameters with the numbers 1 and 2 to tell them apart. We draw a random sample from Population 1 and label the sample statistics it yields with the subscript 1.
How to test a difference in two population means?
Step 1: Determine the hypotheses. The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0, is again a statement of “no effect” or “no difference.” The alternative hypothesis, H a, can be any one of the following.
How big does a sample have to be to be an independent statistic?
The test statistic has the standard normal distribution. The samples must be independent, and each sample must be large: n1 ≥ 30 and n2 ≥ 30. Refer to Example 9.1.1 concerning the mean satisfaction levels of customers of two competing cable television companies.
When is a sample from two distinct populations independent?
Samples from two distinct populations are independent if each one is drawn without reference to the other, and has no connection with the other. Our goal is to use the information in the samples to estimate the difference μ1 − μ2 in the means of the two populations and to make statistically valid inferences about it.