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		1.65	0.55	1.57	0.205
Error	68		24.09	0.35
Total	71		25.74

Level	N	Mean	StDev
Priority Mail Express	18	2.970	0.580
Priority Mail	18	3.042	0.866
First-Class Mail	18	3.335	0.435
Standard Mail	18	3.266	0.377

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 0.05 significance level. (Round your answer to 2 decimal places.)

4. Use the 0.05 significance level to test if this evidence suggests a difference in the means for the different types of mail.

Answer 1

Null hypothesis:

H0: μ1 = μ2 = μ3 = μ4

Alternate hypothesis:

H1: At least one mean is different.

What is the decision rule? Use the 0.05 significance level. (Round your answer to 2 decimal places.)

if p<0.05,reject Ho

if p>0.05,do not reject Ho

Here Fstatistic,F=1.57,p=0.205=0.21(rounded to 2 decimals)

p>0.05

Do not reject Ho.

Accept Ho

Use the 0.05 significance level to test if this evidence suggests a difference in the means for the different types of mail

There is no sufficient statisitcal evidence at 5% level of significance to conclude that there are difference in the means for the different types of mail.