Reject H
0
if the p-value is less than
α
◦
In the trash bag case,
α
was set to 0.05
◦
The calculated p-value of 0.0139 is <
α
= 0.05
This implies that the test statistic z = 2.20 is greater than the
rejection point z
0.05
= 1.645
◦
Therefore reject H
0
at the
α
= 0.05 significance level
LO9-3

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9-40
Steps in Testing a “Less Than”
Alternative in Payment Time Case #1
1.
State the null and alternative hypotheses
◦
In the payment time case, H
0
:
≥
19.5 vs. H
a
:
< 19.5,
where
is the mean bill payment time (in days)
2.
Specify the significance level
α
◦
In the payment time case, set
α
= 0.01
3.
Select the test statistic
◦
In the payment time case, use the test statistic
◦
A negative value of this this test statistic results from a
sample mean that is less than 19.5 days
n
.
x
.
x
z
x
5
19
5
19
LO9-3

9-41
Steps in Testing a “Less Than”
Alternative in Payment Time Case #2
4.
Determine the critical value rule
◦
Decide how much less than 0 test statistic must be to
reject H
0
with probability of
α
◦
The probability
α
is the area in the left-hand tail of the
standard normal curve
◦
Use standard normal table to find the rejection point
–
z
α
◦
Since
α
= 0.01 in the payment time case, the rejection
point is
–
z
α
=
–
z
0.01
=
–
2.33
◦
Reject H
0
in favor of H
a
if the test statistic z is calculated
to be less than the rejection point
–
z
α
◦
In the payment time case, reject H
0
if the test statistic
–
z
is less than
–
2.33
LO9-3

9-42
Steps in Testing a “Less Than”
Alternative in Payment Time Case #3
5.
Collect the sample data and calculate the
value of the test statistic
◦
In the payment time case, assume that
σ
is
known and
σ
= 4.2 days
◦
For a sample of n=65,
x̄
= 18.1077 days:
67
2
65
2
4
5
19
1077
18
5
19
.
.
.
.
n
.
x
z
LO9-3

9-43
Steps in Testing a “Less Than”
Alternative in Payment Time Case #4
6.
Decide whether to reject H
0
by using the test
statistic and the rejection rule
◦
Compare the value of the test statistic to the rejection
point according to the rejection rule
◦
In the payment time case, z =
–
2.67 is less than z
0.01
= -
2.33
◦
Therefore reject H
0
:
μ ≥
19.5 in favor of
H
a
:
μ
< 19.5 at the 0.01 significance level
7.
Interpret the statistical results in managerial
terms and assess their practical importance
◦
Can conclude that the mean bill payment time of the
new billing system is less than 19.5 days
LO9-3

9-44
Steps Using a p-
value to Test a “Less
Than” Alternative
(Steps 1
–
3 are the same)
4.
Collect the sample data and compute the value of
the test statistic
◦
In the payment time case, the value of the test statistic
was calculated to be z =
–
2.67
5.
Calculate the p-value by corresponding to the test
statistic value
◦
In the payment time case, the area under the standard
normal curve in the left-hand tail to the left of the test
statistic z =
–
2.67
◦
The area is = 0.0038
◦
The p-value is 0.0038
LO9-3

9-45
Steps Using a p-
value to Test a “Less
Than” Alternative
Continued
5.