Question

Please help me answer this question for my Statistical Methods subject. PLEASE answer it seriously and completely, or better not answer it if not then, really appreciate it, thank you.

2 The manager of a bank wanted to know whether the four tellers serve, on average, the same number of customers per hour. A research officer of the bank observed each of the four tellers for a certain number of hours. The following table gives the mumber of customers served by the four tellers during each of the observed hours. Teller IV Teller I Teller II Teller III 20 18 13 18 26 16 17 24 21 13 13 26 19 21 14 21 24 14 16 19 11 14 = 21.6 11.3 15.5 14.5 22 2.7 8.5 13.1 - = 18.091 GM By using a 0.05 Test for homogeneity of variances (a) (40 marks) (b) Test the hypothesis that the mean number of customers served per hour by each of these four tellers is the same (30 marks) If the null hypothesis is rejected, test all possible pair wise comparisons (c) for the mean number of customers served. (30 marks)

Answer 1

(a)

Test for Equal Variances: No. of Customers versus Teller

95% Bonferroni confidence intervals for standard deviations

Teller N Lower StDev Upper
I 5 1.53911 2.91548 12.0956
II 6 2.00969 3.61939 12.0274
III 6 0.91238 1.64317 5.4603
IV 5 1.77460 3.36155 13.9462

Bartlett's Test (Normal Distribution)
Test statistic = 2.77, p-value = 0.428

Levene's Test (Any Continuous Distribution)
Test statistic = 1.07, p-value = 0.385
Since p-value>0.05 so we conclude that variances of observations corresponding 4 tellers are equal.

Test for Equal Variances for No. of Customers Bartlett's Test Test Statistic 2,77 P-Value 0.428 Levene's Test Test Statistic 1.07 p-Value 0.385 II IV 2 4 6 8 10 12. 14 95% Bonferroni Confidence Intervals for StDevs Teller

(b)

One-way ANOVA: No. of Customers versus Teller

Source DF SS MS F P
Teller 3 255.62 85.21 9.69 0.000
Error 18 158.20 8.79
Total 21 413.82

Since p-value<0.05 so the mean number of customers served per hour by each of these four tellers are not same.

(c)

Level N Mean StDev ------+---------+---------+---------+---
I 5 22.000 2.915 (-------*-------)
II 6 15.500 3.619 (------*-------)
III 6 14.500 1.643 (------*-------)
IV 5 21.600 3.362 (-------*-------)
------+---------+---------+---------+---
14.0 17.5 21.0 24.5

Pooled StDev = 2.965

Grouping Information Using Tukey Method

Teller N Mean Grouping
I 5 22.000 A
IV 5 21.600 A
II 6 15.500 B
III 6 14.500 B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Teller

Individual confidence level = 98.89%

Teller = I subtracted from:

Teller Lower Center Upper  
II -11.577 -6.500 -1.423
III -12.577 -7.500 -2.423  
IV -5.703 -0.400 4.903   
Since from the above C.I. s we see that C.I. for (Teller II-Teller I) does not contain zero hence Teller I and Teller II are significantly different.   

Teller = II subtracted from:

Teller Lower Center Upper
III -5.841 -1.000 3.841
IV 1.023 6.100 11.177
Since from the above C.I. s we see that C.I. for (Teller IV-Teller II) does not contain zero hence Teller IV and Teller II are significantly different.      

Teller = III subtracted from:

Teller Lower Center Upper  
IV 2.023 7.100 12.177
Since the C.I. for (Teller IV-Teller III) does not contain zero hence Teller IV and Teller III are significantly different.