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STEP BY STEP
Critical Value Approach to Hypothesis Testing
1- State Ho and H1
2- Choose level of significance, α
Choose the sample size, n
3- Determine the appropriate test statistics and sampling distribution.
4- Determine the critical values that divide the rejection and non-rejection areas.
5- Collect the sample data, organize the results and compute the value of the test
statistics.
6- Make the statistical decision and state the managerial conclusion
If the test statistics falls into non-rejection region, DO NOT REJECT Ho
If the test statistics falls into rejection region, REJECT Ho
The managerial conclusion is written in the context of the real world problem.
ACTUAL SITUATION
STATISTICAL DECISION
DO NOT
REJECT H0
REJECT H0
H0 IS TRUE
CORRECT DECISION
1-α
TYPE I ERROR
(α ERROR)
H0 IS FALSE
TYPE II ERROR
( β ERROR)
CORRECT DECISION
1-β
If the null hypothesis is true and accepted or false and rejected
the decision is in either case CORRECT.
If the null hypothesis is true and rejected or false and accepted
the decision is in either case in ERROR.
Exercise - 1
One Tailed Test
TEST at the 5% level whether the single sample value of 172 comes
from a normal population with mean µ= 150 and variance σ2=100.
Exercise –McDonald
One Tailed Test
In one past study, McDonald’s had a mean service time of 174.22 seconds. Suppose that
this company began a quality improvement effort to reduce the service time and selected a
sample of 25 stores. The sample mean has been calculated as 162.96 seconds and sample
standard deviation is 20.2 seconds.
You wish to determine whether the new drive-through process has a mean that is less than
174.22 seconds.
Exercise –Internet Access
Z-test for Proportion
Of 2000 adults, 1540 said that they wanted Internet Access so, they could check personal email while on vacation. A survey conducted in the previous year indicated that 75% of adults
wanted Internet Access.
Is there evidence that the percentage of adults who wanted Internet Access has changed from
the previous year
Exercise – 3
The manager of the women`s dress department of a department
store wants to know whether the true average number of women`s
dresses sold per day is 24.
If in a random sample of 36 days the average number of dresses
sold is 23 with a standard deviation of 7 dresses,
Is there, at the 0.05 level of significance, sufficient evidence to
reject the null hypothesis that µ=24?
Exercise – 4
Exercise – 5
Exercise – Wind Speed
A researcher claims that the average wind speed in
a certain city 8 miles per hour. A sample of 32 days
has an average wind speed of 8.2 miles per hour.
The standard deviation of the sample is 0.6 mile
per hour. At α = 0.05, is there enough evidence to
reject the claim?
Use p-value method.
Exercise – Starting Salary
A job placement director claims that the average
starting salary for nurses is 24,000 USD. A sample
of 10 nurses` salaries has a mean of 23,450 USD
and a standard deviation of 400 USD. Is there
enough evidence to reject the director`s claim at
α=0.05?
Exercise – 6
Exercise – Room Rates
A survey found that the average hotel room rate in
Antalya is 88.42 TL and the average room rate in
Izmir 80.61 TL. Assume that the data were obtained
from two samples of 50 hotels, each and that
standard deviations were 5.63TL and 4.83 TL,
respectively. At α = 0.05, can it be concluded that
there is significant difference in the rates?