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

H0 is select one (not rejected, rejected). There is select one (no significant difference, a significant difference) in the means for the different types of mail

Answer 1

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

identify the null hypothesis and the alternate hypothesis.

1) Null hypothesis:

H0: μ1 = μ2 = μ3 = μ4

2) Alternative hypothesis

H1: At least one mean is different.

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

We reject Ho if P-value < 0.01

From ANOVA table: "P" = 0.157

P-value = 0.157 > 0.01

So we do not reject Ho.

H0 is not rejected. There is no significant difference in the means for the different types of mail.