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      2.41   0.80   2.50   0.067
Error   68      21.58   0.32        
Total   71      23.99           

Level   N   Mean   StDev
Priority Mail Express   18   2.833   0.530
Priority Mail   18   3.350   0.788
First-Class Mail   18   3.099   0.450
Standard Mail   18   3.079   0.406

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:

H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4

H0: μ1 = μ2 = μ3 = μ4

a
b

Alternate hypothesis:

H1: At least one mean is different.
H1: All means are equal.

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

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

from the given data,

Null hypothesis:b)H0: μ1 = μ2 = μ3 = μ4.

Alternate hypothesis:a)H1: At least one mean is different.

The results follow:

Source   DF      SS   MS F P
Factor   3      2.41 0.80   2.50   0.067
Error   68      21.58   0.32        
Total   71      23.99        

p value=0.067.

so, p-value > 0.05.so fail to reject null hypothesis H0.

Therefore, no significant difference between the means.