9: Hypothesis Testing

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One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

9.1: Language of Hypothesis Testing
This page covers hypothesis testing fundamentals, presenting null and alternative hypotheses and their implications. It explains the decision-making process when assessing evidence against the null hypothesis, detailing p-values, alpha levels, critical values, and test statistics. The page also addresses Type I and Type II errors and their probabilities, emphasizing the necessity for rigor in summarizing results and the importance of maximizing test power to ensure reliable outcomes.
9.2: Test for the Population Proportion
This page covers hypothesis testing for a proportion, focusing on evaluating if a population's proportion differs from a known value through the formulation of hypotheses and calculation of a test statistic. It details methodologies, including classical and p-value approaches for conducting two-tailed, right-tailed, and left-tailed tests.
9.3: Test for the Population Mean
This page covers hypothesis testing for a population mean, focusing on the formulation of null and alternative hypotheses, and the use of $z$-tests and $t$-tests. It explains classical and p-value methods for assessing claims, calculating critical values, test statistics, and evaluating $p$-values.

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