Formula Review

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 αp-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: μ=μx¯μ=μx¯ and σx¯=σxn.σx¯=σxn.
  • For a single population proportion, we may use a normal distribution with the following mean and standard deviation. Proportions: µ = p and σ=pqnσ=pqn.