# One way ANOVA test using SAS and analyzing the results

Use the values from the ANOVA table to test the Hypothesis etc.

From time to time, unknown to its employees, the research department at a commercial bank observes various employees for their efficiency. Recently, this department wanted to check whether four tellers at a branch of this bank serve, on average, the same number of customers per hour. The research assistant observed each of the four tellers for a certain number of hours in a given week. The following table gives the number of customers served by the four tellers during each of the observed hours.

Teller A Teller B Teller C Teller D

19 14 11 24

21 16 14 19

26 14 21 21

24 13 13 26

18 17 16 20

13 18

The following ANOVA table was generated from the sample results:

Source of Variation Sum of Squares Degrees of Freedom Mean Square F-ratio

Treatment or Factor SSF=?? k-1=?? MSF=??

Error SSE=?? N-k=?? MSE=??

Total SST=?? N-1=??

a) Copy the ANOVA table above and use a statistical software to compute the missing values of the ANOVA table.

b) Use the values from the ANOVA table to answer the following:

i. What hypothesis is being tested in the problem?

ii. What are the main assumptions of this model?

iii. What conclusion can you draw from the information in the ANOVA Table.

iv. Use the Tukey-Kramer procedure to find out which pairs are different.