Question

Taxpayer	Form 1	Form 2	Form 3	Form 4
1	109	115	126	120
2	98	103	107	108
3	29	27	53	38
4	93	95	103	109
5	62	65	67	64
6	103	107	111	128
7	83	82	101	116
8	122	119	141	143
9	92	101	105	108
10	107	113	127	113
11	103	111	111	108
12	54	64	67	62
13	141	145	142	160
14	92	94	95	102
15	29	32	33	62
16	83	83	89	86
17	34	36	40	48
18	83	86	90	119
19	157	157	172	193
20	99	107	111	100
21	118	123	117	130
22	58	65	75	81
23	66	71	79	81
24	60	60	78	41
25	102	106	100	142
26	128	134	135	142
27	87	93	90	77
28	126	134	129	154
29	133	130	148	164
30	100	112	107	120

Each of the three new forms and the currently used form were filled out by 30 different people. The amount of time (in minutes) taken by each person to complete the task was recorded.

a) Describe the problem background, the objective of the study and identify the type of scale of measurement for the data

b) Use appropriate descriptive statistics to explore and summarize the data for Tax form 2 & 3 and compare their results. Remember to interpret the findings accurately and present them in a clear and coherent way.

Answer 1

(a) The problem is the amount of time taken by each person to complete the task. The objective of the study is to minimize the amount of time taken by each person to complete the task. The scale of measurement is ratio scale.

(b) The descriptive statistics to explore and summarize the data for Tax form 2 & 3 is:

	Form 2	Form 3
count	30	30
mean	95.67	101.63
sample standard deviation	32.57	31.88
sample variance	1,061.06	1,016.59
minimum	27	33
maximum	157	172
range	130	139
1st quartile	73.75	81.50
median	102.00	104.00
3rd quartile	114.50	123.75
interquartile range	40.75	42.25
mode	65.00	111.00

The mean time taken to fill the form 2 is less than form 3. The variation in the filling time is more for form 2. The middle most time to fill out the form is less for form 1.