Question

1. For the question below, please do the following:

a) State the null and alternative hypotheses. (3 pts)

b) Fill in the ANOVA table (Show work to receive full credit. At minimum you must show the formula and what values are substituted in for each element of the formula along with your final answer. You many use Excel to obtain the sums and squared values.) (43 pts – 2 pts each except SS values are 5 pts each)

c) Determine whether your results are significant (2 pts)

d) State your conclusions in one or two sentences. (2 pts)

A supplement was given to 8 subjects with their meal and plasma protein was measured at 3 time points after feeding. Determine if plasma protein changes over time. If results are significant there is no need to do post hoc tests.     

Table 1. Plasma protein measured (mg/ml) at 3 time periods after feeding.

Subject	Time 1	Time 2	Time 3
1	42.8	42.4	38.9
2	43.1	42.2	40.3
3	40.4	40.8	37.5
4	46.6	45.9	42.9
5	42.2	42.4	39.7
6	38.7	38.1	35.8
7	35.3	34.3	32.3
8	40.5	40.1	37.3

ANOVA TALBE TO FILL IN:

Source	Df	SS	MS	F	Critical F
Between	Dfa	SSB
Within	Dfw	SSW
Treatment	Dft	SSTw	MSTw	MSTw/MSEw	XX.XX
Error	Dfe	SSW	MSEw
Total	Dftotal	SST

Answer 1

A supplement was given to 8 subjects with their meal and plasma protein was measured at 3 time points after feeding. Determine if plasma protein changes over time.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 = mu3

H1 : Atleast one population mean differ.

where mu1, mu2 and mu3 are three population mean time.

Assume alpha = level of significance = 0.05

Here we have to test three population means so we use one way anova.

We can do ANOVA in excel.

steps :

ENTER data into excel sheet --> Data --> Data analysis --> Anova : SIngle factor --> ok --> INput range : select all the values together--> Grouped by : columns --> Labels in first row --> Assume alpha : 0.05 --> Output range : select one empty cell --> ok

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Time 1	8	329.6	41.2	11.21714
Time 2	8	326.2	40.775	11.87357
Time 3	8	304.7	38.0875	10.14411
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	45.57583	2	22.78792	2.056992	0.152823	3.4668
Within Groups	232.6438	21	11.07827
Total	278.2196	23

Test statistic = 2.064P-value = 0.1528

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that the population means are equal.

We get insignificant results about F-test.