Question

The postal service sorts mail as Priority Mail Express, Priority Mail, First-Class Mail, or Standard Mail. Over a period of 3 weeks, 18 of each type were mailed from the Network Distribution Center in Atlanta, Georgia, to Des Moines, Iowa. The total delivery time in days was recorded. Minitab was used to perform the ANOVA. The results follow:

Source	DF		SS	MS	F	P
Factor	3		1.30	0.43	1.79	0.157
Error	68		16.45	0.24
Total	71		17.75

Level	N	Mean	StDev
Priority Mail Express	18	2.965	0.345
Priority Mail	18	3.044	0.631
First-Class Mail	18	3.296	0.578
Standard Mail	18	3.231	0.341

Using the ANOVA results, compare the average delivery times of the four different types of mail.

1. Identify the null hypothesis and the alternate hypothesis.

Null hypothesis:

1. H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

2. H₀: μ₁ = μ₂ = μ₃ = μ₄

• a

• b

2. Alternate hypothesis:

• H₁: At least one mean is different.

• H₁: All means are equal.

3. What is the decision rule? Use the 0.01 significance level. (Round your answer to 2 decimal places.)

4. Use the 0.01 significance level to test if this evidence suggests a difference in the means for the different types of mail.

Answer 1

We want to test the average delivery times of the four different types of mail.

Null hypothesis:

H0: μ1 = μ2 = μ3 = μ4

Alternative Hypothesis:

Ha: At least one type of mail has a different average delivery time.

Answer:-

H0: μ1 = μ2 = μ3 = μ4

vs

H1: At least one mean is different.

Q.2)

What is the decision rule? Use the 0.01 significance level.

Decision Rule:

Reject Ho if P-value < 0.01

Q.3)

Use the 0.01 significance level to test if this evidence suggests a difference in the means for the different types of mail.

P-value = 0.157 (from table)

P-value = 0.157 > 0.01

So we fail to reject Ho.

There is not sufficient evidence suggests a difference in the means for the different types of mail.