9.1 Null and Alternative Hypotheses
H0 and Ha are contradictory.
| If H0 has: | equal (=) | greater than or equal to (≥) | less than or equal to (≤) |
| then Ha 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.
9.3 Distribution Needed for Hypothesis Testing
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: and
- For a single population proportion, we may use a normal distribution with the following mean and standard deviation. Proportions: µ = p and .