Question
The owner of two stores tracks the times for customer service in seconds. She thinks store...
The owner of two stores tracks the times for customer service in seconds. She thinks store 1 has longer service times. Perform a hypothesis test on the difference of the means. We know the population standard deviations. (This is rare.)
Population 1 has standard deviation σ1=σ1= 4.5
Population 2 has standard deviation σ2=σ2= 4.5
The populations are normal. Use alph=0.05alph=0.05
Use the claim for the alternate hypothesis.
| Service time store 1 | 174 | 184 | 170 | 174 | 174 | 189 | 174 | 179 | 176 | 173 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Service time store 2 | 163 | 154 | 162 | 164 | 166 | 160 | 162 | 158 | 161 | 157 | 163 |
Choose the null and alternate hypothesis.
- H0:μH0:μ1 −μ-μ2 =0=0
H1:μH1:μ1 −μ-μ2 <0<0 - H0:μH0:μ1 −μ-μ2 =0=0
H1:μH1:μ1 −μ-μ2 ≠0≠0 - H0:μH0:μ1 −μ-μ2 =0=0
H1:μH1:μ1 −μ-μ2 >0>0
The drawing is
- right-tailed
- left-tailed
- two-tailed
What is the mean for set 1?
What is the mean for set 2?
What is the Standard Error, SE?
What is the test statistic? ( (¯x(x¯ 1 - ¯xx¯
2)/SE)
What is the critical value z star? (to accoodate chart use, round zstar to 2 places)
Do you reject or fail to reject?
- Reject the null hypothesis
- Fail to reject the null hypothesis
Homework Answers
Answer #1
H0:μH0:μ1 −μ-μ2 =0=0
H1:μH1:μ1 −μ-μ2 ≠0≠0
It is two tailed test
Mean ( Store 1 ) X̅ = Σ Xi / n
X̅ = 1767 / 10 = 176.7
Mean ( Store 2 ) Y̅ = ΣYi / n
Y̅ = 1770 / 11 = 160.9091
Standard Error = 
= 1.9662
Test Statistic :-
Z = 8.03
Critical value Z(α/2) = Z(0.05 /2) = 1.96
Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2)
| Z | > Z(α/2) = 8.0312 > 1.96
Result :- Reject Null Hypothesis
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