# Hypothesis Testing: ANOVA and Kruskal Wallis Test

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1 There are four McDonalds restaurants in a particular area. The numbers of burgers sold at the respective restaurants for each of the last 4 days are shown below.

Restaurant

1 2 3 4

Day 1 81 79 55 36

2 83 69 65 45

3 67 59 58 62

4 77 69 73 58

Restaurant sum of squares= 1793.25

Day sum of squares= 250.25

Total sum of squares= 2841.75

i) Construct ANOVA table for the above data.

ii) Test at the 5% significance level to determine if differences exist among the restaurants

iii) Test at the 5% significance level to determine if differences exist among the four days

iv) Calculate Tukey's criticalnumber w at the 5% level of significance and perform the comparison between Restaurant 1 and 2

2 Bank A is interested in determining how long it takes one of its tellers to complete a transaction as compared to two other banks B and C. The following results were obtained.

Time to complete transaction

Bank A Bank B Bank C

12 23 15

14 8 20

11 17 21

16 9 7

10 13 22

24

Using Kruskal- wallis test, determine whether there is any difference in the completion time of these banks. Use alpha = 5%

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