You are given a six-faced die and asked to determine with 95% confidence if it is “fair.”

• What are the hypotheses?

Answer: the null H₀: the die is fair, p₁ = p₂ = … = p₆ = 1/6; the alternative Ha: the die is not fair, at least one p_i ≠ 1/6.

• What is the critical value of chi-square?

Answer: degrees of freedom df = 6 – 1 = 5. From a table or calculator, χ_0.05² =11.071.

Common student mistake #1:Example problem re: Goodness of Fit test: