- Complete a two-sample [latex]t[/latex]-test for independent population means from hypotheses to conclusions
Difference of the Means
One way to compare the means of two groups is by looking at the difference of the means.
When we are interested in estimating a difference in population means using data from independent samples, we will use a two-sample [latex]t[/latex] confidence interval or a two-sample [latex]t[/latex]-test.
conditions for two-sample [latex]t[/latex]-test
- The samples are independent.
- Each sample is a random sample from the corresponding population of interest, or it is reasonable to regard the sample as random. It is reasonable to regard the sample as a random sample if it was selected in a way that should result in a sample that is representative of the population. If the data are from an experiment, we just need to check that there was random assignment to experimental groups—this substitutes for the random sample condition and also results in independent samples.
- For each population, the distribution of the variable that was measured is approximately normal, or the sample size for the sample from that population is large. Usually, a sample of size [latex]30[/latex] or more is considered to be “large.” If a sample size is less than [latex]30[/latex], you should look at a plot of the data from that sample (a dotplot, a boxplot, or, if the sample size isn’t really small, a histogram) to make sure that the distribution looks approximately symmetric and that there are no outliers.