Download QMS 202 Hypothesis Testing - Basic Procedures a] Identify the

QMS 202 Hypothesis Testing - Basic Procedures
Step 1.
a]
b]
Identify the statement about a population Parameter that is to be tested.
If the statement above involves a strict inequality [ #,<,>] then formulate
the alternative hypothesis, H1
ie: H1: µ =/ 10 or H1: µ<10 or H1: π >.3
or if the statement in part a] involves an equality [=, > , < ] then formulate the null hypothesis, H0
ie: H0: µ = 10 or H0: µ < 10 or H0: π > .3
c]
Formulate the complementary Hypothesis to that determined in b].
ie: if b] was H0: µ< 10 then H1: µ > 10
if b] was H1: π < .2 then H0: π > .2
QMS 202 Hypothesis Testing - Basic Procedures
Step 2:
Assume the Null hypothesis is true, identify a test statistic associated with the population parameter
which will be useful in choosing the correct Hypothesis.
Step 3:
Select a significance level, α. If the null hypothesis, H0, is rejected, α is the maximum acceptable is
the probability that H0 is in fact true, a Type I error.
Usually α is set to .05 but can be made larger or smaller if the penalties for making a Type I and/or
Type II* error warrant a change. If α is decreased, the probability of a Type II error increases and
visa versa.
A Type II error occurs when a false H0 is accepted.
QMS 202 Hypothesis Testing - Basic Procedures
Step 4:
Check Conditions then
Classical Method:
Obtain the required sample/sample statistics and calculate the specified test statistic, ie: z calc.
Using α, identify the critical value(s) for the test statistic, ie: z crit, and the rejection regions for the
null hypothesis. If H1 involves either <, or > then there will only be a one tail test, upper or lower;
however, if H1 uses =/ then the rejection region will be on each side of test statistic distribution ie: a
2-tailed test.
If zcalc is unusual with respect to zcrit , reject H0 , otherwise fail to reject H0 .
p-Value Method:
Obtain the required sample/sample statistics and calculate the specified test statistic, ie: z calc.
Determine the p-value for this test statistic, ie: probability of obtaining the test statistic or beyond.
(double this value for a two tail test).
If the test statistic is unusual, ie the p-value is smaller than α, then the assumption on which the test
is based is unreasonable, ie: reject H0 . [Note that H0 might still be true and the unusual test statistic
could have occurred by chance, then a Type I error would have occurred, this has a probability of α]
If the test statistic is not in the “rejection region” then fail to reject H0 , [Note that H0 might not be
true, then a Type II error would have occurred, The probability of this is β the value of which
depends on the true value of µ]
QMS 202 Hypothesis Testing - Basic Procedures
Step 6:
State the conclusion in the context of the original statement that was being tested.
Actual Situation
H 0 True
H 0 False
Fail to
Reject H0
U
Type II Error
Reject H0
Type I Error
"Level of Significance"
α
U
Decision
QMS 202 Hypothesis Testing - Basic Procedures
Single-Sample Hypothesis Test
Population Mean µ
0 normal
ie: x normal and/or n > 30 [Note #1]
σknown
Population Proportion π
p normal
ie: nπ and n(1-π) are> 5 [Note #2]
σ unknown
Notes:
# 1: If the population is not known to be at least approximately normally distributed and the sample size
is < 30 then the Central Limit Theorem does not apply and hypothesis tests are more complicated
because test statistics are dependent on the specific population distribution or must be distribution
free.
# 2: If symmetry conditions are not satisfied then hypothesis tests of B are complicated because they are
based on specific skewed binomial distributions.
# 3: For all three formulae, if the population size is small compared to the sample size, ie: n >N/20
{unusual} , then the “standard deviation” in the test statistic formulae should be multiplied by the
Finite Population correction factor: