Download Significance Test for a Population Mean µ 1. Assumptions Randomization 2. Hypotheses

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Transcript
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.