- Check the assumptions for a one-sample [latex]t[/latex] confidence interval for population mean.
- Calculate a confidence interval for a population mean and explain what it means.
Making Inferences about a Population Mean
As was the case with previous inference methods, there are a few assumptions/conditions that you should check before using the one-sample [latex]t[/latex]-interval. Two important ones are:
- The sample is a random sample from the population of interest, or it is reasonable to regard the sample as if it were a random sample. 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.
- The population distribution of the variable that was measured is approximately normal, or the sample size is large. Usually, a sample of size [latex]30[/latex] or more is considered to be “large.” If the sample size is less than [latex]30[/latex], you should look at a plot of the data (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.