Question

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

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