Question

A national dairy manufactures products at facilities throughout the US. To test the uniformity of its products four local sites were randomly chosen and samples of margarine produced at these sites were analyzed to determine the level of a particular fatty acid as a percentage of the fats. The data are recorded in the table below.

(i): Test the hypothesis.

(ii): Analyze with one-way ANOVA to test the hypothesis that there is any significant differences in the heights among the three fertilizer treatments at both:

(a): 95% and 90% level of significance.

Site
A	B	C	D
13.5	13.2	16.8	18.1
13.4	12.7	17.2	17.2
14.1	12.6	16.4	18.7
14.2	13.9	17.3	18.4
55.2	52.4	67.7	72.4
Sum of sums of X(ij) square = 3907.2

Answer 1

Ho : There is no significant differences in the heights among the three fertilizer treatments .
Ha : Atleast two fertilizers are significantly different in the heights.

Decision Criteria : Reject Ho if F > F crit
where F crit = F( ,k-1, n-k) = F(0.05,3,16) = 3.2389 at 5% l.o.s
and F crit = F( ,k-1, n-k) = F(0.10,3,16) = 2.4618 at 10% l.o.s

Calculation : The results for this data can be obtained by using the MS-Excel and by for this, we need to follow the below given steps and they are :

Step 1 : Enter the data in MS-Excel.
Step 2 : Select the "Anova : Single Factor" function from the data analysis package available under the data tab of MS-Excel.
Step 3 : Enter the range of the data in the first cell and the l.o.s. in the second cell.
Step 4 : Click ok.

For = 0.05,

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	5	110.4	22.08	342.917
B	5	104.8	20.96	309.163
C	5	135.4	27.08	515.747
D	5	144.8	28.96	590.013
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	223.222	3	74.40733333	0.169315372	0.915530385	3.238871517
Within Groups	7031.36	16	439.46
Total	7254.582	19

Here, F < F crit

For = 0.10,

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	5	110.4	22.08	342.917
B	5	104.8	20.96	309.163
C	5	135.4	27.08	515.747
D	5	144.8	28.96	590.013
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	223.222	3	74.40733333	0.169315372	0.915530385	2.461810753
Within Groups	7031.36	16	439.46
Total	7254.582	19

Here too, F < F crit

Conclusion : Since in both the cases F < F crit, we do not reject Ho at 5% and 10% l.o.s. and thus conclude that there is no significant differences in the heights among the three fertilizer treatments.

Hope this answers your query!