The Steps to Performing Hypothesis Testing - Write the original claim and identify whether it is the null hypothesis or the alternative hypothesis.
- Write the null and alternative hypothesis. Use the alternative hypothesis to identify the type of test.
- Write down all information from the problem.
- Find the critical value using the tables
- Compute the test statistic
- Make a decision to reject or fail to reject the null hypothesis. A picture showing the critical value and test statistic may be useful.
- Write the conclusion.
Null Hypothesis (H0) Statement of zero or no change. If
the original claim includes equality (<=, =,
or >=), it is the null hypothesis. If the original claim does not
include equality (<, not equal, >)
then the null hypothesis is the complement of the original claim. The null
hypothesis always includes the equal sign. The decision is based on the
null hypothesis. Alternative Hypothesis (Ha or H1) Statement which is true if the null
hypothesis is false. The type of test (left, right, or two-tail) is based on
the alternative hypothesis. Left Tailed TestH:
parameter < valueNotice the inequality points to the left
Decision Rule: Reject H if t.s. < c.v. Right Tailed TestH:
parameter > valueNotice the inequality points to the right
Decision Rule: Reject H if t.s. > c.v. Two Tailed TestH:
parameter not equal valueAnother way to write not equal is < or > Notice the inequality points to both sides
Decision Rule: Reject H if t.s. < c.v. (left) or t.s. > c.v. (right) Type I error Rejecting the null hypothesis when
it is true (saying false when true). Usually the more serious error. Type II error Failing to reject the null hypothesis
when it is false (saying true when false). Probability of committing a Type I error.alpha Probability of committing a Type II error.beta Test statisticSample statistic used to decide
whether to reject or fail to reject the null hypothesis. Critical region Set of all values which would cause
us to reject H0 Critical value(s) The value(s) which separate the
critical region from the non-critical region. The critical values are
determined independently of the sample statistics. Significance level ( alpha ) The probability of rejecting the
null hypothesis when it is true. alpha = 0.05 and alpha = 0.01 are common. If
no level of significance is given, use alpha = 0.05. The level of significance
is the complement of the level of confidence in estimation. Decision A statement based upon the null
hypothesis. It is either "reject the null hypothesis" or "fail
to reject the null hypothesis". We will never accept the null hypothesis. Conclusion A statement which indicates the
level of evidence (sufficient or insufficient), at what level of significance,
and whether the original claim is rejected (null) or supported (alternative). |