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		4.19	1.40	6.36	0.001
Error	68		14.66	0.22
Total	71		18.85

Level	N	Mean	StDev
Priority Mail Express	18	2.847	0.414
Priority Mail	18	3.392	0.478
First-Class Mail	18	3.472	0.535
Standard Mail	18	3.190	0.420

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

Identify the null hypothesis and the alternate hypothesis.

Null hypothesis:

a) H₀: ?₁ ? ?₂ ? ?₃ ? ?₄

b) H₀: ?₁ = ?₂ = ?₃ = ?₄

Alternate hypothesis:

H₁: At least one mean is different.

H₁: All means are equal.

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

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

Null hypothesis:

all 4 group means are equal

Alternative Hypothesis:

Atleast one of the means are different.

H1: At least one mean is different.

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

p<0.01 reject null hypohesis

if p>0.01 do not reject null hypothesis

here p=0.001

and p<0.01

Reject null hypothesis

there is sufficient evidence at 1% level of significance that it suggests a difference in the means for the different types of mail.