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```HYPOTHESIS TESTING
WHAT IS HYPOTHESIS TESTING?
Hypothesis testing
Based on
sample
evidence and
probability
theory
Used to determine whether
the hypothesis is a
reasonable statement and
should not be rejected, or
is unreasonable and should
be rejected
A statistical
hypothesis is an
assertion or
conjecture
concerning one or
more populations.
What is a
Hypothesis?
Graduate school students sleep
less than the average person.
A certain peanut butter manufacturer is
under filling jars so the mean content is less than 32
oz.
STEPS IN TESTING HYPOTHESES
1. Establish hypotheses: state the null and
alternative
.
2. Select the level of significance ( 
3. Determine the appropriate statistical
and
sampling distribution.
4. State the
.
5. Gather sample data. Calculate the value of the
test statistic.
6. Make a
.
7. State the statistical
. Make a
managerial decision.
9-4
STEP 1: ESTABLISH HYPOTHESES: STATE THE
NULL AND ALTERNATIVE
.
Null and alternate hypotheses
Null Hypothesis
H0
A statement
about the value
of a population
parameter
Alternative
Hypothesis Ha:
A statement that is
accepted if the
sample data provide
evidence that the null
hypothesis is false
Three forms of the null and alternate
hypotheses
The null
hypothesis
always contains
equality.
H0: m = 0
Ha: m  0
H0: m1 = m2
Ha: m1  m2
H0: m = 0
Ha: m > 0
H0: m1 = m2
Ha: m1 > m2
H0: m = 0
Ha: m < 0
H0: m1 = m2
Ha: m1 < m2
Example
Determine the null and alternative hypotheses in the following
statements.
1. According to Giving and Volunteering in the United States,
2001 Edition, the mean charitable contribution per
household in the US in 2000 was \$1623. A researcher
believes that the level of giving has changed since 2000.
2. Federal law requires that jars of peanut butter labeled as
containing 32 oz. must contain at least 32 oz. A consumer
advocate feels that a certain peanut butter manufacturer is
underfilling jars so the mean contents are less than 32 oz.
3. According to the Centers for Disease Control and
Prevention, 16% of children aged 6 to 11 years are
overweight. A school nurse thinks the percentage of 6- to
11-year-olds who are overweight is higher in her district.
STEP 2:. SELECT THE LEVEL OF
SIGNIFICANCE ( 
Level of Significance.
Null
Hypothesis
Ho is true
Ho is false
Researcher
Accepts
Rejects
Ho
Ho
Correct
Type I
error
decision
(a
Type II
Correct
Error
Decision
(power)
(b
RISK
TABLE
Notation:
a = P(Type I Error) = P(rejecting Ho when Ho is
true)
b = P(Type II Error) = P(not rejecting H0 when Ha
is true)
1- β = power of the test= P(rejecting Ho when Ho
is false)
Remark: the probability of making a Type I error,
is called the level of significance.
STEP 3: DETERMINE THE APPROPRIATE
STATISTICAL
AND SAMPLING
DISTRIBUTION
SOME TEST STATISTICS
T-test
 Z-test
 F-test
 Chi-square

13
STUDENT'S T-TEST
A test of the null hypothesis that the means of
two normally distributed populations are equal.
 A test of whether the mean of a normally
distributed population has a value specified in
a null hypothesis.
 A test of whether the slope of a regression line
differs significantly from 0.

14
Assumptions
 normal distribution of data (e.g. Wilk-Shapiro
normality test, KS-test)
 equality of variances (F test, or more robust Levene's
test)
 Samples may be independent or dependent,
depending on the hypothesis and the type of samples:
 Independent samples are usually two, randomly
selected groups
 Dependent samples are either two groups matched
on some variable (for example, age) or are the same
people being tested twice (called repeated measures)
15
Z-TEST
The z value is based on the sampling distribution of
X, which is normally distributed when the sample is
reasonably large (recall Central Limit Theorem).
 data points should be independent from each
other
 the distributions should be normal if n is low, if
however n>30 the distribution of the data does not
have to be normal
 the variances of the samples should be the same
 all individuals must be selected at random from
the population
16
F TEST FOR TWO POPULATION
VARIANCES
S
F
S
2
1
2
2
dfnumerator   1  n1  1
dfdenom inator   2  n2  1
17
F-TEST FOR ONE WAY ANALYSIS OF VARIANCE
(ANOVA)
MSC
F
MSE
(
x

SST   x 
n
(
( x )
x

SSC  SSb  

2
2
2
2
i
ni
SSE  SST  SSC
SSC
MSC 
dfc
n
MSE 
SSE
dfe
STEP 4: . STATE THE
DECISION RULE FOR
ONE-TAILED TESTS
Rejection Region
Non Rejection Region
m=12 oz
Critical Value
Reject Ho if
Computed < - Critical Value
Rejection Region
y
m=12 oz
Critical Value
Reject Ho if
Computed > Critical
value
DECISION RULE FOR
TWO-TAILED TESTS
Rejection
Region
Rejection
Region
Non Rejection Region
m=12 oz
Critical Values
Reject Ho if
Computed  > Critical Value
9-21
USING THE P-VALUE IN HYPOTHESIS TESTING
p-Value
Calculated from
the probability
distribution
function or by
computer
The probability, assuming
that the null hypothesis is
true, of finding a value of the
test statistic at least as
extreme as the computed
value for the test
Decision Rule
If the p-Value is larger
than or equal to the
significance level, a, H0 is
not rejected.
If the p-Value is
smaller than the
significance level, a,
H0 is rejected.
Step 6: Make a decision.
MOVIE
STEP 7: STATE THE STATISTICAL
.
STATING THE CONCLUSION OF A HYPOTHESIS
TEST
The sample evidence of a hypothesis testing
situation enable us to decide whether to reject
or not reject the null hypothesis.
 If we do not reject the null hypothesis, we are
not saying the null hypothesis is true, only that
it could be true.

THANK YOU FOR LISTENING!
```
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