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.
(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.
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