Download Significance Tests about Hypotheses

Significance Tests about Hypotheses
Hypothesis
In statistics, a hypothesis is a statement about a population,
usually of the form that a parameter takes a particular numerical
value or falls in a certain range of values
Null hypothesis H0 and alternative hypothesis Ha .
A significance test is a method for using data to summarize the
evidence about a hypothesis.
Steps for a Significance Test
1. Assumptions
2. Hypotheses: null hypothesis H0 and alternative hypothesis Ha
3. Test statistic
4. P-value
5. Conclusion
Significance Test for a Population Proportion p
1. Assumptions
Randomization, and large sample size
2. Hypotheses
Null: H0 : p = p0
Alternative: Ha : p > p0 (one-sided) or Ha : p < p0
(one-sided) or Ha : p 6= p0 (two-sided)
3. Test statistic
z=
p̂ − p0
se0
with se0 =
p
p0 (1 − p0 )/n
4. P-value
Alternative hypothesis
Ha : p > p 0
Ha : p < p 0
Ha : p 6= p0
5. Conclusion
P-value
Right-tail probability
Left-tail probability
Two-tail probability
More on P-values
Alternative hypothesis Ha : p > p0
1-prob, where prob is the probability corresponding to the
z-score
Alternative hypothesis Ha : p < p0
prob, where prob is the probability corresponding to the
z-score
Alternative hypothesis Ha : p 6= p0
2 × prob, where prob is the probability corresponding to the
z-score if z-score is negative;
2 × (1 − prob), where prob is the probability corresponding to
the z-score if z-score is positive
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.