Question

follow the 10-step hypothesis testing procedure, in the step of"calculation of test statistie, use MATLAB to obtain the ANOVA table and find the results accordingly If the post analysis is needed, use MATLAB function ‘muitcompare". Attach all MATLAB results/figures and draw your conclusion accordingly. · Ilich-Ernst et al. investigated dietary intake of calcium among a cross section of 105 healthy women ages 20-88. The researche four age groupings as follows rs rormed Group A, 20.0-45.9 years; Group B, 46.0-55.9 years; Group C, 56.0-65.9 years; Group D, over 66 years Calcium from food intake was measured in mg/day. The data below are consistent with summary statistics (1) Do these data provide sufficient evidence to indicate a difference in mean calcium intake among (2) If the null hypothesis is rejected, perform the post analysis to identify which pair(s) of age groups given in the paper age groups? have different mean calcium intake? 3 5 5 6 77 3 3 3 4 433 69 624 99 4 3 5710 7 4389 08 77 6579 9943 60 2 2 2 4 9 4 1

Answer 1

data

A	B	C	D
1820	191	724	1652
2588	1098	613	1309
2670	644	918	1002
1022	136	949	966
1555	1605	877	788
222	1247	1368	472
1197	1529	1692	471
1249	1422	697	771
1520	445	849	869
489	990	1199	513
2575	489	429	731
1426	2408	798	1130
1846	1064	631	1034
1088	629	1016	1261
912		1025	42
1383		948	767
1483		1085	752
1723		775	804
727		1307	1182
1463		344	1243
1777		961	985
1129		239	1295
		944	1676
		1096	754
		1020	775
		805	1393
		631	533
		641	734
		760	485
			449
			236
			831
			698
			167
			824
			448
			991
			590
			994
			1781

1)

Anova one way is used

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	22	31864	1448.363636	395799.4805
B	14	13897	992.6428571	393458.8626
C	29	25341	873.8275862	92868.57635
D	40	34398	859.95	157664.2026
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	5667260.704	3	1889086.901	8.603804265	3.85497E-05	2.694618
Within Groups	22175978.34	101	219564.142
Total	27843239.05	104

p-value = 0.0000385 < alpha

hence we reject the null hypothesis

we conclude that there is difference in mean calcium intake among age groups

2)

Tukey HSD Post-hoc Test...
Group 1 vs Group 2: Diff=-455.7208, 95%CI=-874.2084 to -37.2332, p=0.0272
Group 1 vs Group 3: Diff=-574.5360, 95%CI=-920.6200 to -228.4521, p=0.0002
Group 1 vs Group 4: Diff=-588.4136, 95%CI=-913.3222 to -263.5050, p=0.0000
Group 2 vs Group 3: Diff=-118.8153, 95%CI=-517.1773 to 279.5467, p=0.8637
Group 2 vs Group 4: Diff=-132.6929, 95%CI=-512.8031 to 247.4174, p=0.7985
Group 3 vs Group 4: Diff=-13.8776, 95%CI=-312.4174 to 284.6622, p=0.9992

when p-value is less than 0.05

the pair have different mean calcium intake

here

(1,2) , (1,3),(1,4) are significantly different