GSBA 545: Hypothesis Testing
A two-sided hypothesis test is appropriate when the context of the situation either
(1) does NOT indicate any expected direction results, or (2) indicates BOTH directions are to be assessed.
Hypothesis Testing Steps
1. Determine null and alternative hypotheses. 2. Specify level of significance α. 3. Calculate test statistic value. 4. Determine critical value(s) or calculate the p-value. 5. Decide whether to reject H0 and interpret the statistical result in (real-world) managerial terms.
Type II Error:
Failing to reject H0 when it is false
For 2 sided testing (CI approach) the rejection rule for null is:
If the CI does contain µ0, do NOT reject H0. If the CI does not contain µ0, reject H0.
Large Sample, 2 sided tests: rejection rules
Reject H0 if z < -za/2 or if z > za/2.
Type I Error:
Rejecting H0 when it is true
A two-sided hypothesis can also be tested with
a confidence interval calculation.
P values: reject H0 if
if the p-value < a
Null hypothesis, denoted H0
is a statement of the basic proposition being tested. The statement generally represents the status quo and is not rejected unless there is convincing sample evidence that it is false.
Alternative or research hypothesis, denoted Ha
is an alternative (to the null hypothesis) statement that will be accepted only if there is convincing sample evidence that it is true.
critical value
is the corresponding Z value from a standard normal table corresponding to a desired level of significance a
Small Sample testing: reject H0 if
• Lower tail: Reject H0 if t < -ta,n-1 • Upper tail: Reject H0 if t > ta,n-1 • Two-sided: Reject H0 if |t| > ta/2,n-1
For large sample, one-sided tests, The rejection rules for H0 are:
• Lower tail: Reject H0 if z < -za • Upper tail: Reject H0 if z > za
A p-value is
• The smallest level of a for which the null hypothesis can be rejected. • The area under the curve beyond the calculated test statistic, in the direction of the alternative hypothesis. • The level of support for the null hypothesis being true.