QM201 TA Section 1
Jieling Han
Ch10 Hypothesis Testing
1. GOAL (USE µ AS AN EXAMPLE)
Goal: Decide between two possibilities (about the population parameter)
 Null hypothesis H0: µ=µ0 (States the prior value of the parameter)
 Research hypothesis H1: µ≠ µ0 (Negates the null hypothesis)
 µ0 is called reference/stated value
2. HOW TO DECIDE (USE µ AS AN EXAMPLE)
Confidence Interval (e.g 95% or 5% test level): Is µ0 in [ X  tS X , X  tS X ]?


Yes, accept Ho
o The sample average is not significantly different from the stated value µ0 (likely
an estimation error)
o A weak/not strong conclusion, since the probability of making Type II Error
cannot be estimated / controlled.
No, reject Ho and accept H1
o The sample average is significantly different from the stated value µ0 (likely a
material error)
o A strong conclusion, since the probability of making Type I Error can be
estimated / controlled.
3. ERRORS IN HYPOTHESIS TESTING (USE 5% TEST LEVEL AS AN EXAMPLE)
TRUTH
DECISION
NULL HYPOTHESIS: H0
RESEARCH HYPOTHESIS: H1
ACCEPT H0
CORRECT DECISION
TYPE II ERROR
The probability of making Type II Error
CANNOT be determined.
REJECT H0, AND ACCEPT H1
TYPE I ERROR
CORRECT DECISION
Using 5% test level / 95% CI, the
probability of making Type I Error is
5%.
Only 95% chance the CI contains µ, so
5% chance the CI doesn’t contain µ,
which is the probability of making Type
I Error.
Ch10 Hypothesis Testing