Complete a one-sample [latex]t[/latex]-test for means from hypotheses to conclusions.
Notation for population mean: [latex]\mu[/latex] (pronounce as “mu”)
Notation for sample mean: [latex]\bar{x}[/latex] (pronounce as “x-bar”)
Conditions for a One-Sample [latex]t[/latex]-Test
The sample is a random sample from the population of interest or it is reasonable to regard the sample as if it is 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.
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.