Question

1. A dataset was randomly from a 4-component uniform mixture and it is below.   Are the group different at the 10% significance level?  X is the outcome variable (which are the numbers under every group).

Group 1	Group 2	Group 3	Group 4
60	98	96	47
44	96	46	47
54	90	72	57
86	54	53	95
82	96	60	92
78	53	46	95
79	68	61	64
50	90	49	72
53	34	42	71
88	91	53	63
69	65	66	74
56	36	61	46
94	70	96	38
41	48	100	80
70	54	99	92
88	60	76	93
67	77	81	95
65	77	67	51
93	81	64	84
65	53	77	92
93	96	73	62
56	47	49	47
84	32	84	86
74	76	70	74
37	41	95	74
77	86	84	77
34	91	57	86
43	71	92	99
87	64	93	91
36	55	61	96
58	59	42	99

2. Is there an appropriate alternative statistical analysis method to answer question 1?  Justify.  If yes, perform the alternative analyses

I have done the ANOVA test for the first question but I do not know about the second question. Please answer both questions so I can make sure it is right! thank you!

Answer 1

As an alternative statistical analysis method, one can perform paired t tests to check which means are significantly different.

Since P-value for all 6 tests are > 0.05, so at 5% level of significance, we can conclude that there is no significant difference in means of four groups.