Question

A national bank that is developing very rapidly will impose a new mechanism in customer service. For this reason, trials were conducted at several branch offices. If from the trial it turns out consumers are more satisfied then the new mechanism will be applied to all of its branch offices. 24 customers were chosen to be asked for their opinion on the new mechanism. Their answer is to compare to various elements of the new mechanism with existing ones. There are 3 elements assessed, namely ease, speed, and convenience of the transaction. In each element there are several measurement measures. The various assessment measures of the 3 elements are combined into a single ordinal scale that shows the comparison of the quality of service, between new and existing ones. The scale value ranges from -7 to +7. The greater number indicates the assessment of the quality of the new mechanism which is better than the existing method. A zero value means there is no difference between the two service mechanisms. The following data is from a trial customer:

Number	score difference
1	-2
2	4
3	5
4	1
5	0
6	-5
7	3
8	4
9	-1
10	6
11	-5
12	0
13	-1
14	7
15	2
16	1
17	-5
18	3
19	6
20	-2
21	5
22	-5
23	7
24	-3

Based on the sample data, test that customers tend to prefer new mechanisms over existing ones, using a confidence level of 98%.

Answer 1

Ho : There is no difference between the two service mechanisms i.e   = 0
Ha : Customers tend to prefer new mechanisms over existing ones i.e. > 0

In general, (1-)% confidence level for population difference is obtained as follows :

where t (/2, n-1) = t (0.01,23) = 2.499867.
and = 1.041667 and s = 4.005205

Thus, 98% confidence level for population difference is :

( -1.002122 , .3.085456 )
Since the 98% confidence level for population difference consists of zero, we do not reject Ho at 5% l.o.s. and thus, conclude that there is no difference between the two service mechanisms i.e   = 0.

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