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.

Here, F = 2.911

F > 2.739502 , so reject null hypothesis ( H0)

There is ample evidence to indicate a disparity in the means for the different forms of mails.

Step-by-step explanation:

Null hypothesis -  H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternative hypothesis - H₁: At least one mean is different.

df1 is factor degree of freedom and df2 is error degree of freedom.

Decision rule -  Reject H₀ if F > F₀.₀₅, (df1, df2)

F0.05, df1,df2   is f critical value at \alpha = 0.05

Here df1 = 3 , and df2 = 68

Using Excel,

F₀.₀₅, ₃, ₆₈ = FINV( 0.05, 3 , 68 ) = 2.739502302

So reject H0 if F > 2.739502

Here, F = 2.911

F > 2.739502 , so reject null hypothesis ( H0)

There is ample evidence to indicate a disparity in the means for the different forms of mails.