Hypothesis Testing

Hypothesis testing is a statistical method for making decisions about population parameters. The null hypothesis (H₀) represents the status quo, while the alternative hypothesis (H₁) represents the claim being tested. Type I error (α) is rejecting H₀ when it is true. Type II error (β) is failing to reject H₀ when it is false. The p-value is the probability of observing the test statistic or more extreme under H₀. If p-value < α, reject H₀.

Governing FormulaZ = (x̄ - μ₀)/(σ/√n), t = (x̄ - μ₀)/(s/√n), p-value = P(Z > |Z_test|)

Knowledge Check

10 Questions

1.A test has H₀: μ = 100 vs H₁: μ ≠ 100. The sample mean is 105, n=36, σ=12. What is the Z-statistic?

2.What is the probability of a Type I error in hypothesis testing?

3.If the p-value is 0.03 and α = 0.05, what is the decision?

4.A Type II error is defined as:

5.What is the power of a statistical test?

6.A one-tailed test is used when:

7.The significance level (α) is typically set at:

8.A sample has n=25, x̄=52, s=8, and H₀: μ=50. What is the t-statistic?

9.If the test statistic falls in the rejection region, we:

10.The p-value is the smallest significance level at which: