Question

We want to test the hypothesis that ‘Education (Years)’ differs by ‘Ethnicity’. Have Minitab or Statcrunch perform an ANOVA test to determine this.

a) Write the hypotheses using symbols and words. Choose a significance level.

b) Check the conditions for the test (you might want to do part (c) first). If the conditions fail, make a statement about this, but perform the test anywa

c) Include the output from Minitab or Statcrunch after performing the test.

d) Determine whether to reject or fail to reject the null hypothesis.

e) State your conclusion in words relating to the statement of the question.

Age (Years)	Education (Years)	Gender	Student	Married	Ethnicity	Income (Dollars/Year)			Income of Females	Income of Males
71	14	Female	No	Yes	Asian	29705			29705	18145
56	15	Male	No	Yes	African American	18145			55412	49502
37	16	Female	Yes	Yes	Caucasian	55412			20974	140672
44	16	Female	No	Yes	Caucasian	20974			30550	13647
81	9	Female	No	No	African American	30550			75406	103893
55	14	Male	No	Yes	Caucasian	49502			12000	10635
46	9	Male	No	Yes	African American	140672			30007	15741
41	14	Female	No	Yes	Asian	75406			152298	44205
47	14	Male	No	Yes	Caucasian	13647			87625	42529
28	14	Female	No	Yes	Caucasian	12000			30682	17316
69	9	Female	No	Yes	Caucasian	30007			31335	32856
41	12	Female	No	Yes	Asian	152298			19782	60449
84	17	Male	No	No	Asian	103893			130209	149316
69	16	Male	No	Yes	Asian	10635			27470	11603
46	10	Female	No	No	African American	87625			28575	83869
39	14	Male	No	Yes	Asian	15741			34509	24050
77	7	Female	No	No	Caucasian	30682			58351	107841
38	7	Female	No	No	Caucasian	31335			15079	33017
46	16	Female	Yes	No	Caucasian	19782			30413	29567
39	19	Female	No	Yes	Caucasian	130209			80616	26370
32	12	Male	No	Yes	Caucasian	44205			57337	24824
32	11	Female	No	Yes	Asian	27470			94193	30012
37	11	Male	No	Yes	Asian	42529			69165	36364
65	13	Male	No	No	African American	17316			27369	15717
60	11	Female	No	No	African American	28575			58929	30111
80	18	Female	No	Yes	African American	34509			59879	35691
68	13	Male	No	No	Caucasian	32856			44473	91362
69	8	Male	No	Yes	Caucasian	60449			37878	28144
80	16	Male	No	No	African American	149316			16103	52179
85	16	Female	No	Yes	Caucasian	58351			53401	25124
71	11	Male	No	Yes	Caucasian	11603			10588	68713
28	15	Female	No	Yes	Asian	15079			31811	62328
83	11	Male	No	No	African American	83869			26067	69656
32	18	Male	No	Yes	Caucasian	24050			19537	44522
87	7	Male	No	No	African American	107841			36496	71682
28	16	Male	No	Yes	African American	33017			24230	16304
25	15	Female	Yes	No	Asian	30413			23350	23793
25	15	Male	No	No	Caucasian	29567			26532	23672
57	7	Female	No	Yes	Asian	80616			29403	27229
78	11	Male	No	Yes	Asian	26370			148924	60579
45	7	Female	No	No	Caucasian	57337			22939	13561
33	9	Male	Yes	No	Caucasian	24824			22561	53480
33	17	Male	No	Yes	Caucasian	30012			106025	55882
44	16	Female	No	Yes	Caucasian	94193			65896	28508
34	11	Female	No	No	African American	69165			80861	12414
40	9	Female	No	Yes	Caucasian	27369			29638	23949
66	9	Female	No	Yes	African American	58929			15846	23857
78	15	Female	No	No	Caucasian	59879			15333	14887
81	16	Female	No	No	African American	44473			32164	16479
50	19	Male	No	No	Caucasian	36364			20936	33437
38	16	Male	Yes	Yes	Caucasian	15717			55187	125480
80	13	Female	No	No	Caucasian	37878			59855	24889
81	18	Male	No	Yes	Caucasian	30111			21455	36362
45	10	Female	No	Yes	Caucasian	16103			14084	67937
35	15	Male	No	No	African American	35691			41419	83851
47	17	Male	No	Yes	Asian	91362			27272	25974
35	12	Female	No	No	African American	53401			63931	43682
66	13	Female	No	Yes	Caucasian	10588			40885	20405
75	13	Female	No	Yes	Caucasian	31811			19144	64173
74	17	Female	No	Yes	African American	26067			20089	35610
51	10	Male	No	Yes	Caucasian	28144			27847	85425
57	14	Male	No	No	Asian	52179			18951	91876
34	9	Female	No	Yes	Asian	19537			49927	41400
29	12	Male	No	Yes	Caucasian	25124			13676	76348
56	16	Male	Yes	No	Caucasian	68713			98515	23012
83	15	Male	No	No	Caucasian	62328			10735	15354
41	14	Male	No	Yes	African American	69656			27794	160231
72	15	Male	No	Yes	Asian	44522			58165	121709
57	16	Male	No	Yes	Caucasian	71682			36508	68462
69	15	Female	No	Yes	Asian	36496			73914	113772
66	10	Male	No	Yes	Asian	16304			41025	21153
70	14	Male	No	No	African American	23793			36934	41532
63	11	Male	No	No	Caucasian	23672			134181	31367
51	11	Male	No	No	Caucasian	27229				76782
38	15	Male	No	Yes	Asian	60579				30733
64	15	Female	No	Yes	Caucasian	24230				53308
49	12	Female	Yes	No	Caucasian	23350				55054
58	19	Female	No	Yes	Caucasian	26532
37	19	Male	No	Yes	Asian	13561
83	15	Male	No	No	Caucasian	53480
68	16	Male	No	Yes	Caucasian	55882
56	14	Male	No	Yes	Asian	28508
37	14	Female	No	Yes	Caucasian	29403
36	11	Female	No	No	Asian	148924
32	12	Male	No	Yes	African American	12414
47	18	Female	No	Yes	Asian	22939
40	18	Male	No	Yes	African American	23949
56	16	Male	No	Yes	Caucasian	23857
58	12	Male	No	Yes	African American	14887
66	15	Female	No	No	Caucasian	22561
82	15	Female	Yes	Yes	Asian	106025
49	17	Female	No	Yes	Caucasian	65896
29	15	Female	No	Yes	Asian	80861
26	16	Male	No	No	African American	16479
29	15	Female	No	Yes	Asian	29638
44	9	Male	Yes	No	Caucasian	33437
53	12	Female	No	No	Caucasian	15846
82	16	Male	No	Yes	Caucasian	125480
75	12	Male	No	Yes	Caucasian	24889
47	9	Female	No	Yes	Asian	15333
79	15	Female	No	Yes	African American	32164
30	15	Female	No	No	Asian	20936
50	17	Female	No	Yes	Caucasian	55187
49	15	Male	No	Yes	African American	36362
63	12	Male	No	Yes	Asian	67937
47	18	Male	No	No	Caucasian	83851
46	13	Female	No	Yes	Caucasian	59855
24	10	Male	No	No	Asian	25974
49	9	Male	No	Yes	Caucasian	43682
72	17	Male	Yes	No	Asian	20405
80	12	Female	No	Yes	African American	21455
46	17	Female	No	Yes	African American	14084
80	10	Male	No	Yes	Caucasian	64173
40	12	Male	No	No	Caucasian	35610
60	12	Male	No	Yes	African American	85425
24	11	Female	Yes	No	Caucasian	41419
33	10	Male	No	Yes	Caucasian	91876
67	10	Female	No	Yes	Caucasian	27272
36	14	Male	No	Yes	Caucasian	41400
60	18	Male	No	No	Asian	76348
28	14	Female	No	Yes	African American	63931
81	16	Male	No	No	Caucasian	23012
46	13	Female	No	Yes	African American	40885
65	14	Male	No	No	Asian	15354
69	17	Male	No	No	Caucasian	160231
75	13	Female	No	No	African American	19144
57	15	Female	No	Yes	African American	20089
50	6	Male	No	Yes	Caucasian	121709
78	15	Female	No	Yes	Caucasian	27847
71	16	Male	No	Yes	Caucasian	68462
82	13	Female	No	No	Caucasian	18951
75	17	Female	No	Yes	Caucasian	49927
69	15	Male	Yes	Yes	Caucasian	113772
41	11	Male	No	No	Caucasian	21153
50	12	Male	No	Yes	Caucasian	41532
30	10	Male	No	Yes	Caucasian	31367
44	12	Male	No	Yes	Asian	76782
51	13	Male	No	No	Caucasian	30733
80	16	Female	No	No	African American	13676
78	11	Female	No	No	African American	98515
44	17	Female	No	Yes	Caucasian	10735
35	8	Female	No	Yes	African American	27794
84	10	Male	No	Yes	Caucasian	53308
56	12	Female	No	Yes	Caucasian	58165
74	17	Male	No	Yes	Asian	55054
79	6	Female	No	Yes	Caucasian	36508
67	15	Female	No	Yes	Caucasian	73914
79	19	Female	No	Yes	Caucasian	41025
63	9	Female	No	Yes	Caucasian	36934
48	13	Female	No	No	Caucasian	134181

Answer 1

First sort out data in education according to Ethnicity .
Factor level 3 as , African American, Asian, Caucasian

=mean for African American , = mean for Asian , = men for Caucasian .

Hypothesis :

Null hypothesis : Mean for all three factor are equal .

Alternative hypothesis : At least mean not equal .

     Vs

Level of significance = 0.05

----------------------

Minitab output :

So here , p- value for the factor = 0.681   > level of significance = 0.05 .

Decision : Fail to reject H0.

Conclusion : At 5% level of significance we say that all means are equal .

                     That is at 5% level of significant we conclude that ANOVA is significant .