Statistics

# Formula Review

StatisticsFormula Review

### 9.1Null and Alternative Hypotheses

 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.

### 9.2Outcomes 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.

### 9.3Distribution 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: $μ= μ x ¯ μ= μ x ¯$ and $σ x ¯ = σ x n . σ x ¯ = σ x n .$
• For a single population proportion, we may use a normal distribution with the following mean and standard deviation. Proportions: µ = p and $σ= pq n σ= pq n$.