9.1 Null and Alternative Hypotheses

H₀ and H_a are contradictory.

If H₀ has:	equal (=)	greater than or equal to (≥)	less than or equal to (≤)
*then H_a* has:**	not equal (≠) or greater than (>) or less than (<)	less than (<)	greater than (>)

Table 9.4

If α ≤ p-value, then do not reject H₀.

If α > p-value, then reject H₀.

α is preconceived. Its value is set before the hypothesis test starts. The p-value is calculated from the data.

9.2 Outcomes and the Type I and Type II Errors

α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

If there is no given preconceived α, then use α = 0.05.

Types of Hypothesis Tests

Single population mean, known population variance (or standard deviation): Normal test.
Single population mean, unknown population variance (or standard deviation): Student's t-test.
Single population proportion: Normal test.
For a single population mean, we may use a normal distribution with the following mean and standard deviation. Means: $μ = μ_{\bar{x}}$ and $σ_{\bar{x}} = \frac{σ_{x}}{\sqrt{n}} .$
For a single population proportion, we may use a normal distribution with the following mean and standard deviation. Proportions: µ = p and $σ = \sqrt{\frac{p q}{n}}$ .