Population when the
σ
is Known
Example: Soda Bottles 2
Step 5: Determine whether to reject
H
0
p
≤ α
, which means there is little evidence supporting the
H
0
. So, we reject the null hypotheses

Testing a Hypothesis about a
Population when the
σ
is Unknown
•
If we
don’t know
the population standard deviation (
σ
) we use a t-
test.
•
t-test is also very simple:
•
t =
ҧ𝑥− 𝜇
0
𝑠/√𝑛
•
X-bar: sample mean
•
μ
0
: hypothesized population mean
•
s: sample standard deviation
•
n: sample size

Testing a Hypothesis about a
Population when the
σ
is Unknown
Example: Customer Satisfaction
A restaurant manager wants to know if customers are happy with the
services provided by the restaurant. To do so, they decide to ask
customers to rate their overall satisfaction with the restaurant on a
scale of 1 to 7. The manager will decide that they are doing fine if the
average score is not less than 5. A group of 64 randomly selected
consumers are asked to rate their overall satisfaction with the
restaurant on a scale of 1 to 7. The average satisfaction rating was 4.91
with a sample standard deviation of 1.34.
The restaurant manager wants to perform a hypothesis test, with a .05
level of significance, to determine if the average satisfaction rating is
not significantly less than 5.

Testing a Hypothesis about a
Population when the
σ
is Unknown
Example: Customer Satisfaction
Step 1: Develop the hypotheses
H
0
:
μ
≥
5
H
a
:
μ
< 5
Step 2: Determine the level of significance
α
= 0.05

Testing a Hypothesis about a
Population when the
σ
is Unknown
Example: Customer Satisfaction
Step 3: Compute the test statistic
t =
ҧ𝑥− 𝜇
0
𝑠/√𝑛
=
=
4.91−5
1.34/√64
= -0.54
Step 4: Compute the p-value
0
t
.05
= -1.669
-.54
p-value > .20

Testing a Hypothesis about a
Population when the
σ
is Unknown
Example: Customer Satisfaction
Step 5: Determine whether to reject
H
0
p
>
α
, which means we cannot reject the null hypothesis

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- Fall '17
- AMHET KOKSUEL