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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.
ACCEPT H0
H0 IS TRUE
H0 IS FALSE
REJECT H0
CORRECT DECISION
TYPE I ERROR
(α ERROR)
TYPE II ERROR
(β ERROR)
CORRECT DECISION
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.
Example : Fast-Food Restaurant
You are manager of a fast-food restaurant. You want to determine whether the waiting
time to place an order has changed in the past month from its previous population mean
value of 4.5 minutes.
A-) State the null Hypothesis and Alternative Hypothesis
From past experience, you can assume that the population is normally distributed with
the standard deviation of 1.2 minutes. You select a sample of 25 orders during one-hour
period. The sample mean is 5.1 minutes.
B- Determine whether there is evidence at the 0.05 level of significance that the
population mean waiting time to place an order has changed in the past month from its
previous population mean value of 4.5 minutes.
C- Find and use p-Value approach to test the Hypothesis.
Exercise - 1
One Tailed Test
TEST at the 5% level whether the single sample value of 172 comes
from 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 –Fast Food
One Tailed Test for Proportion
A fast food chain has developed a new process to ensure that orders at the drive-through
are filled correctly. The business problem is defined as determining whether the new
process can increase the percentage of orders processed correctly. The previous process
filled orders correctly 85% of the time.
Data are collected from a sample of 100 orders using the new process. The results indicate
that 94 orders were filled correctly. At the 0.01 level of significance, can you conclude that
the new process has increased the proportion of orders filled correctly?
Exercise - 2
One Tailed Test
TEST at the 1% level whether the single sample value 54 has been
drawn from a normal population with mean 65 and variance 30 or
whether the mean is less than 65.
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 – 6
Exercise – 7