Section 7.5: Testing a Claim About a Mean: \(\sigma\) Unknown

1. Compare and contrast the density histograms for the standard normal distribution and the \(T\)-distribution with df degrees of freedom.
2. Compute a \(T\)-statistic when given a sample mean, sample standard deviation, and sample size for a simple random sample.
3. Determine the sampling distribution of the \(T\)-statistic when the null hypothesis about the population mean is true for a random sample of size \(n\) from the population.
4. Determine how the sampling distribution of the \(T\)-statistic behaves as the sample size \(n\) increases.
5. Specify the requirements necessary for the \(T\)-based hypothesis test of a population mean to be valid.
6. Given a claim and sample data, determine whether the \(T\)-based hypothesis test is appropriate to test the claim.
7. Use the T-table from Appendix A–3 of Triola and Triola to determine the critical values / rejection regions for the \(T\)-statistic when testing a null hypothesis using a rejection region of size / significance level \(\alpha\).
8. Given a claim and summary statistics about a data set, perform a \(T\)-based hypothesis test for the claim about the population mean.