For our statistical report we will look at the heights of male and female participants from a selected sample dataset. This dataset will have information on the gender, and the height of the participants which will be used to conduct our subsequent research. All heights measured were in centimeters and based on the result of the tabulated data we will provide a null hypothesis question which will either be affirmed or refuted by the statistical inference that will follow in this report. For an initial perspective we would need to quantify the result in tabulated form which can be noted at the below table:
| No | Height | Gender | No | Height | Gender |
|
1 |
178 |
M |
17 |
166 |
F |
|
2 |
167 |
F |
18 |
163 |
F |
|
3 |
172 |
F |
19 |
170 |
F |
|
4 |
160 |
F |
20 |
175 |
M |
|
5 |
154 |
F |
21 |
158 |
F |
|
6 |
172 |
M |
22 |
183 |
F |
|
7 |
157 |
F |
23 |
163 |
F |
|
8 |
173 |
M |
24 |
173 |
F |
|
9 |
167 |
M |
25 |
155 |
F |
|
10 |
158 |
F |
26 |
157 |
F |
|
11 |
200 |
F |
27 |
162 |
F |
|
12 |
157 |
F |
28 |
173 |
F |
|
13 |
172 |
F |
29 |
165 |
F |
|
14 |
158 |
F |
30 |
178 |
M |
|
15 |
170 |
F |
31 |
171 |
M |
|
16 |
158 |
F |
32 |
158 |
F |
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This table has a total of thirty two participants that were selected using a ballot scheme and hence produced a completely unbiased result. The random sampling done in the above dataset was conducted by writing the name of the entire population on small chits of paper and then procuring them blind folded from a box. This methods produced participants that were purely based on a random selection. There were a total of thirty two selected participants out of which 7 were male and the remaining 25 were female. To develop a simple null hypothesis question we would first need to identify a correlation or a statement that would explain the dataset. From our perspective our null hypothesis question would be as follows:
N 0, which can be attributed as the Null Hypothesis question, showcases that the average height of male participants is more than its female counterparts. To prove or refute this statement we would need to conduct statistical inference on the above dataset using mean and standard deviation however before we indulge into providing these metrics we would first need to quantify height of males and females separately. Below is the tabulated results.
|
Male |
|
|
No |
Height |
|
1 |
178 |
|
2 |
172 |
|
3 |
173 |
|
4 |
167 |
|
5 |
175 |
|
6 |
178 |
|
7 |
171 |
|
Mean |
173.43 |
|
Standard Deviation |
3.66 |
|
Female |
|||
| No | Height | No | Height |
|
1 |
167 |
13 |
166 |
|
2 |
172 |
14 |
163 |
|
3 |
160 |
15 |
170 |
|
4 |
154 |
16 |
158 |
|
5 |
157 |
17 |
183 |
|
6 |
158 |
18 |
163 |
|
7 |
200 |
19 |
173 |
|
8 |
157 |
20 |
155 |
|
9 |
172 |
21 |
157 |
|
10 |
158 |
22 |
162 |
|
11 |
170 |
23 |
173 |
|
12 |
158 |
24 |
165 |
|
25 |
158 |
||
|
Mean |
165.16 |
||
|
Standard Deviation |
10.06 |
||
The results clearly show that the mean height for males is more than height of females. The data tabulated above was quantified using the following expression and the inference was made based on the results procured from the latter.
Arithmetic Mean
Standard Deviation
