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Significance Test for a Population Mean µ 1. Assumptions Randomization 2. Hypotheses Null: H0 : µ = µ0 Alternative: Ha : µ > µ0 (one-sided) or Ha : µ < µ0 (one-sided) or Ha : µ 6= µ0 (two-sided) 3. Test statistic t= x̄ − µ0 se0 √ with se0 = s/ n 4. P-value (Use t distribution with Alternative hypothesis Ha : µ > µ0 Ha : µ < µ0 Ha : µ 6= µ0 5. Conclusion df = n − 1) P-value Right-tail probability Left-tail probability Two-tail probability More on P-values Alternative hypothesis Ha : µ > µ0 or Ha : µ < µ0 p, where p is the probability corresponding to the absolute value of the t-score (the subscript for t in table A-3) Alternative hypothesis Ha : µ 6= µ0 2 × p, where p is the probability corresponding to the absolute value of the t-score if the t-score is negative More on Conclusions If the P-value is less than a preset value (threshod), e.g. 0.05, which corresponds to 95% confidence level, then we reject the null hypothesis. If the P-value is larger than a preset value (threshod), then we do not reject the null hypothesis.