Answer:
H0 is rejected, Hence the true average DNA content is affected by the type of carbohydrate in the diet between samples
Step-by-step explanation:
<u> A B C D E</u>
<u>2.58 2.63 2.13 2.41 2.49</u>
∑A=2.58 ∑B=2.63 ∑C=2.13 ∑D=2.41 ∑E=2.49
<u>A² B² C² D² E²</u>
<u>6.6564 6.9169 4.5369 5.8081 6.2001</u>
∑A²=6.6564 ∑B²=6.9169 ∑C²=4.5369 ∑D²=5.8081 ∑E²=6.2001
Calculations
<u>Group A B C D E Total</u>
<u>N n1=1 n2=1 n3=1 n4=1 n5=1 n=5</u>
∑xi T1=2.58 T2=2.63 T3=2.13 T4=2.41 T5=2.49 ∑x=12.24
<u>∑x²i 6.6564 6.9169 4.5369 5.8081 6.2001 ∑x²=30.1184</u>
<u>Mean xi 2.58 2.63 2.13 2.41 2.49 Total2.448</u>
Σ Σ xij^2 = 185.4 given
Let k = the number of different samples = 5
n=n1+n2+n3+n4+n5=1+1+1+1+1=5
Overall ˉx=12.24/5 =2.448
∑x=T1+T2+T3+T4+T5=2.58+2.63+2.13+2.41+2.49=12.24----1
Correction Factor=(∑x)²/n=12.242/5=29.9635--------(2)
∑T²i/ni=(2.582/1+2.632/1+2.132/1+2.412/1+2.492/1)=30.1184------(3)
∑x²=∑x²1+∑x²2+∑x²3+∑x²4+∑x²5
=6.6564+6.9169+4.5369+5.8081+6.2001=30.1184-------(4)
ANOVA:
Step-1 : sum of squares between samples
SSB=(∑T2i/ni)-(∑x)2/n
=(3)-(2)
=30.1184-29.9635
=0.1549
Step-2 : Total sum of squares
SST=SSB-CF
= 185.4-2.488
=182.952
Step-3 : Sum of Squares Within Samples
SSW=∑x²-(∑T²i/ni)=SST- SSB=
= 182.952-0.1549=182.7971
Step-4 : variance between samples
MSB=SSB/k-1
=0.1549/4
=0.0387
Step-5 : variance within samples
MSW=SSW/n-k
=182.7971/5-5
=36.55942
Step-6 : test statistic F for one way ANOVA test
F=MSB/MSW
=0.0387/36.55942 = 0 .001058
<u>ANOVA table</u>
Source Sums Degrees Mean
of Variation of Squares of freedom Squares
SS DF MS F
B/w samples SSB = 0.1549 k-1 = 4 MSB = 0.0387 0.001
<u>Within samples SSW = 0 n-k = 0 MSW = 36.55942 </u>
<u>Total SST = 0.1549 n-1 = 4 </u>
H0 : The true average DNA content is not affected by the type of carbohydrate in the diet between samples
Ha : The true average DNA content is affected by the type of carbohydrate in the diet between samples
F(4,0) at 0.05 level of significance =0.5
As calculated F=0.001 >0.5
So, H0 is rejected, Hence the true average DNA content is affected by the type of carbohydrate in the diet between samples
