Question

USE R software

Suppose that we want to test H₀ : F = G, where F is the distribution of weight for the casein feed group and G is the distribution of weight for the sunflower feed group of the chickwts data. A test can be based on the two-sample Kolmogorov-Smirnov statistic

chickwts
weight feed
1 179 horsebean
2 160 horsebean
3 136 horsebean
4 227 horsebean
5 217 horsebean
6 168 horsebean
7 108 horsebean
8 124 horsebean
9 143 horsebean
10 140 horsebean
11 309 linseed
12 229 linseed
13 181 linseed
14 141 linseed
15 260 linseed
16 203 linseed
17 148 linseed
18 169 linseed
19 213 linseed
20 257 linseed
21 244 linseed
22 271 linseed
23 243 soybean
24 230 soybean
25 248 soybean
26 327 soybean
27 329 soybean
28 250 soybean
29 193 soybean
30 271 soybean
31 316 soybean
32 267 soybean
33 199 soybean
34 171 soybean
35 158 soybean
36 248 soybean
37 423 sunflower
38 340 sunflower
39 392 sunflower
40 339 sunflower
41 341 sunflower
42 226 sunflower
43 320 sunflower
44 295 sunflower
45 334 sunflower
46 322 sunflower
47 297 sunflower
48 318 sunflower
49 325 meatmeal
50 257 meatmeal
51 303 meatmeal
52 315 meatmeal
53 380 meatmeal
54 153 meatmeal
55 263 meatmeal
56 242 meatmeal
57 206 meatmeal
58 344 meatmeal
59 258 meatmeal
60 368 casein
61 390 casein
62 379 casein
63 260 casein
64 404 casein
65 318 casein
66 352 casein
67 359 casein
68 216 casein
69 222 casein
70 283 casein
71 332 casein

Answer 1

The hypothesis is performed in R. The screenshot is shown below,

R Code:

R Output:

Hypothesis:

The null hypothesis is defined as the two distribution are from the same population and the alternative hypothesis tests the claim that the two distribution are not from the same population.

This is a two-tailed test.

Let the significance level = 0.05

Test statistic and P-value

From the Two-sample Kolmogorov-Smirnov test result summary,

The test statistic, D = 0.3333

P-value = 0.5176

Conclusion:

Since the p-value = 0.5176 > 0.05 at a 5% significance level, the null hypothesis is not rejected hence there is no evidence to conclude that the two distribution are not from the same population.