A bank would like to know if there is a difference in how quickly tellers proces

Question

A bank would like to know if there is a difference in how quickly tellers process a certain transaction. Six tellers were observed processing the transaction and their times were recorded. Use an appropriate statistical method to determine if there is a difference between tellers. If there is a difference, perform a post hoc analysis to determine which teller is fastest. Write a brief summary of your analysis that would be suitable for an email to your boss.

Time Teller 45.1 1 47.8 1 82.6 1 69.5 1 47.3 1 60.2 1 65.4 1 75.1 1 73.9 1 71.9 1 52.8 1 63 1 100.8 1 65.6 1 49.2 2 65.3 2 87.5 2 85.7 2 59.2 2 68.5 2 98.7 2 78.8 2 13.7 2 88.3 2 49.8 2 96.6 2 98.7 2 100 2 108.1 2 85.9 2 79.5 2 121.4 2 86.2 2 83.6 2 56.1 2 93.4 2 83.9 2 92 3 100.3 3 65.5 3 76.4 3 78.9 3 81.8 3 55.5 3 121.1 3 74.6 3 76.1 3 86.3 3 87.6 3 78.2 3 110.2 3 55.4 3 94.8 4 72.2 4 81.8 4 134.2 4 83.2 4 89.3 4 68.9 4 50.4 4 77.2 4 52.6 4 53.2 4 48.3 4 105 4 89.9 4 68.9 4 105.3 5 73.5 5 60.9 5 59.1 5 65.3 5 66.3 5 50.4 5 85.1 5 92.2 5 101.9 5 84 5 114 5 108.9 5 92.7 5 94.6 5 75.5 5 86.3 5 102.3 5 38 5 55.5 5 89.6 5 45.9 5 83 5 88.3 5 74.3 5 44.7 5 46.8 5 106.6 5 98.7 5 97.5 5 80.9 5 117.2 5 83 5 63.5 5 122.9 5 57.8 5 84.3 5 92.2 5 120.2 5 95.9 5 68.6 5 67.9 5 73.7 5 80.8 5 111.9 6 44.7 6 67 6 78.7 6 49.9 6 64.1 6 44.8 6 94.2 6 95 6 41.8 6 61 6 84.8 6 100.2 6 57.9 6 83.4 6 83.8 6 92.8 6 41.7 6 65.5 6 73.8 6 100 6 103.8 6 85.9 6 50 6 87 6 98 6 79.3 6 66 6 76.9 6

Explanation / Answer

One way ANOVA

we can analyse the above problem by using the onen way anocva

hypothesis

H0: all tellers has equal time for procesing.

H1: all tellers has a diffreant processing time.

Hypothesis,

The hypotheses of interest in an ANOVA are as follows:

for Groups,

by using the excel we can solve the problem,

out nut is

data

and excel output is

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

3315.318

5

663.0637

1.508009

0.191432

2.281814

Within Groups

58919.09

134

439.6947

Total

62234.4

139

The p-value of data is grater than 0.05 , we fail to reject the null hypothesis and conclude that there is not any significant diffreance between the all tellers

so we cant do host hoc ananlysis.

thanks

Teller1 Teller2 Teller3 Teller4 Teller5 Teller6 45.1 49.2 92 94.8 105.3 111.9 47.8 65.3 100.3 72.2 73.5 44.7 82.6 87.5 65.5 81.8 60.9 67 69.5 85.7 76.4 134.2 59.1 78.7 47.3 59.2 78.9 83.2 65.3 49.9 60.2 68.5 81.8 89.3 66.3 64.1 65.4 98.7 55.5 68.9 50.4 44.8 75.1 78.8 121.1 50.4 85.1 94.2 73.9 13.7 74.6 77.2 92.2 95 71.9 88.3 76.1 52.6 101.9 41.8 52.8 49.8 86.3 53.2 84 61 63 96.6 87.6 48.3 114 84.8 100.8 98.7 78.2 105 108.9 100.2 65.6 100 110.2 89.9 92.7 57.9 108.1 55.4 68.9 94.6 83.4 85.9 75.5 83.8 79.5 86.3 92.8 121.4 102.3 41.7 86.2 38 65.5 83.6 55.5 73.8 56.1 89.6 100 93.4 45.9 103.8 83.9 83 85.9 88.3 50 74.3 87 44.7 98 46.8 79.3 106.6 66 98.7 76.9 97.5 80.9 117.2 83 63.5 122.9 57.8 84.3 92.2 120.2 95.9 68.6 67.9 73.7 80.8

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