Transcript Your favorite professional football team (I shall refer to them as the

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.
Exercise –Hourly wage
The president of a company states that the average hourly wage of his/her employees is
8.65 TRL. A sample of 50 employees has the distribution shown below. At α=0.05, is the
president’s statement believable? Assume σ=0.105 TRL
Class
8.35-8.43
8.44-8.52
8.53-8.61
8.62-8.70
8.71-8.79
8.80-8.88
Total:
Freq.
2
6
12
18
10
2
50
M
8.39
8.48
8.57
8.66
8.75
8.84
fM
16.78
50.88
102.84
155.88
87.5
17.68
431.56
fM2 _______
140.7842
431.4624
881.3388
1349.9208
765.625
156.2912
3725.4224
Exercise – Athletic Shoes
A researcher claims that the average cost of men`s athletic shoes is less than 80 USD. He
selects a random sample of 36 pairs of shoes from a catalog and finds the following costs. Is
there enough evidence to support the researcher`s claim at α = 0.10. Assume σ=19.2
60
70
75
55
80
55
50
40
80
70
50
95
120
90
75
85
80
60
110
65
80
85
85
45
75
60
90
90
60
95
110
85
45
90
70
70
∑x =2700
Exercise – Life Guards
A researcher wishes to test the claim that the
average age of lifeguards in a city is greater than 24
years. She selects a sample of 36 guards and finds
the mean of the sample to be 24.7 years with a
standard deviation of 2 years. Is there evidence to
support the claim at α = 0.05?
Use p-value method.
Exercise – Assist. Prof.
A researcher reports that the average salary of
assistant professors is more than 42,000 TL. A
sample of 30 assistant professors has a mean salary
of 43,260 TL. At α = 0.05, Test the claim that
assistant professors earn more than 42,000 TL a
year. The population standard deviation is 5,230 TL.
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 – Sugar
Sugar is packed in 5 kg bags. An inspector suspects
the bags may not contain 5 kg. A sample of 50 bags
produces a mean of 4.6 kg and a standard
deviation of 0.7 kg.
Is there enough evidence to conclude that the bags
do not contain 5 kg as stated at α = 0.05?
Also find the 95% CI of the true mean.
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 - 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