Y |
X1 |
X2 |
X3 |
21.87838 |
70.60643 |
32.53764 |
16.41044 |
93.77804 |
24.77081 |
92.403 |
93.99289 |
72.82208 |
22.38328 |
81.0025 |
34.85534 |
9.280099 |
34.70495 |
26.33653 |
61.68477 |
31.1062 |
61.91305 |
51.84463 |
92.25529 |
92.64739 |
17.90097 |
72.9859 |
44.74383 |
81.74105 |
36.03165 |
79.02588 |
59.32679 |
89.92953 |
21.51851 |
34.83117 |
11.82339 |
78.49144 |
48.2808 |
65.38289 |
27.14759 |
65.12506 |
73.91513 |
45.78317 |
48.29154 |
63.9783 |
42.63024 |
51.48476 |
80.61577 |
23.76638 |
81.84579 |
87.52321 |
47.18775 |
52.7846 |
14.18943 |
23.4629 |
82.91467 |
31.50099 |
90.70568 |
88.84991 |
27.21473 |
45.53072 |
54.93847 |
39.86673 |
86.99951 |
35.69863 |
27.72768 |
80.01956 |
21.69039 |
9.978362 |
58.42174 |
61.50215 |
54.04685 |
94.04123 |
72.2205 |
50.09629 |
66.52428 |
93.1308 |
51.50087 |
12.27189 |
22.93652 |
42.10923 |
68.76678 |
35.29041 |
23.17554 |
8.30253 |
9.043764 |
71.03076 |
26.70983 |
7.993683 |
7.451186 |
86.30393 |
28.6408 |
61.24702 |
31.66482 |
50.4105 |
20.05216 |
13.86984 |
75.09412 |
26.66686 |
76.40739 |
31.21632 |
94.43333 |
62.68383 |
81.74642 |
72.60186 |
13.43745 |
58.10215 |
48.42045 |
43.08142 |
70.58226 |
8.592578 |
12.14566 |
75.33583 |
72.40043 |
12.83587 |
22.06638 |
86.41136 |
30.24949 |
89.20978 |
85.65938 |
86.0864 |
38.26341 |
68.98163 |
60.13248 |
29.57002 |
22.18455 |
52.75237 |
54.18918 |
75.3412 |
32.919 |
24.846 |
11.76699 |
40.81475 |
42.46641 |
80.46269 |
9.629231 |
60.65081 |
92.06461 |
36.30021 |
28.46623 |
8.383099 |
14.21897 |
55.42189 |
25.32136 |
38.21238 |
18.43272 |
89.10504 |
35.03259 |
71.59474 |
42.34019 |
30.41063 |
72.5186 |
57.48445 |
38.01633 |
54.26438 |
91.54628 |
62.92822 |
63.21558 |
46.74731 |
35.85708 |
86.75781 |
59.27039 |
62.37498 |
62.31858 |
61.14228 |
33.42927 |
8.127964 |
91.84439 |
21.7629 |
87.34864 |
52.95111 |
87.89651 |
For the given data set, used in question 1; test the hypothesis that the means of variables (Y, X1 and X2) are same by using any 0.04 level of significance. Report the Excel output as well.
The hypothesis being tested is:
H0: µ1 = µ2 = µ3
Ha: At least one means is not equal
The Excel output is:
Mean | n | Std. Dev | |||
53.09780 | 42 | 28.124428 | Y | ||
46.74999 | 42 | 25.343434 | X1 | ||
53.35913 | 42 | 24.482758 | X2 | ||
51.06897 | 126 | 26.002528 | Total | ||
ANOVA table | |||||
Source | SS | df | MS | F | p-value |
Treatment | 1,176.611051 | 2 | 588.3055256 | 0.87 | .4222 |
Error | 83,339.821006 | 123 | 677.5595204 | ||
Total | 84,516.432058 | 125 |
The p-value is 0.4222.
Since the p-value (0.4222) is greater than the significance level (0.04), we fail to reject the null hypothesis.
Therefore, we can conclude that the means of variables (Y, X1 and X2) are the same.
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