Question

5. The following observations were made about the leaf hopper insect's body mass versus the altitude at which it was caught in balloon mounted nets. Carry out a model utility test at a significance level of 1.00%. 900 Mass x Altitude y 10.5 1000 12.6 9.1 1200 11.0 1000 13.0 1100 9.0 1300 16.0 1200 13.0 900 12.3 800 12.0 1200 1000 14.2 800 9.0

Answer 1

S.No х (x-x)? (y-7) 1 2 3 4 5 6 7 8 9 10 11 12 Total Mean 10.5 12.6 9.1 11 13 9 16 13 12.3 12 у 1000 900 1200 1000 1100 1300 1200 900 800 1200 1000 800 12400 1.7117 0.6267 7.3351 0.6534 1.4201 7.8867 17.5701 1.4201 0.2417 0.0367 7.8867 5.7201 52.5092 1111.11 17777.78 27777.78 1111.11 4444.44 71111.11 27777.78 17777.78 54444.44 27777.78 1111.11 54444.44 306666.6667 (x-x)(y-7) 43.6111 -105.5556 -451.3889 26.9444 79.4444 -748.8889 698.6111 - 158.8889 -114.7222 31.9444 93.6111 -558.0556 -1163.3333 14.2 141.7 11.808 1033.3333 SSX SSY SXY

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ≠		0

0.01 level,two tail test and n-2= 10 df, critical t=3.169			(from excel:tinv(0.01,10)
Decision rule: reject Ho if absolute value of test statistic |t|>3.1693
0.01 level,two tail test and n-2= 10 df, critical r=0.708
correlation r='Sxy/(√Sxx*Syy) =		-0.290
test stat t=	r*(√(n-2)/(1-r2))=	-0.958
P value    =	0.3607	(from excel:tdist(0.9579,10,2)

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have sufficient evidence at 0.01 level to conclude that there is a significant correlation between mass and altitude,