Question

Eleven adult black bears were used to evaluate the relationship between age and weight of adult black bears. Age was measured in years and weight was measured in pounds. Here is the data:

age 11 7 11 7 8 7 6 8 12 10 6

weight 119 88 112 121 123 136 92 88 130 112 110

The sample size for this analysis is n =___?____
The correlation coefficient, rounded to three places, is r =___?____
The test statistic for testing whether the age and weight of adult bears is positively correlated is: t(__?___) =___?____, when rounded to 2 places.
The p-value is ___?___ when rounded to three places.

Answer 1

X	Y	XY	X²	Y²
11	119	1309	121	14161
7	88	616	49	7744
11	112	1232	121	12544
7	121	847	49	14641
8	123	984	64	15129
7	136	952	49	18496
6	92	552	36	8464
8	88	704	64	7744
12	130	1560	144	16900
10	112	1120	100	12544
6	110	660	36	12100
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
93	1231	10536	833	140467

Sample size, n =	11
SSxx = Ʃx² - (Ʃx)²/n =	46.7273
SSyy = Ʃy² - (Ʃy)²/n =	2706.91
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	128.455

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 0.361183 = 0.361

Null and alternative hypothesis:

Ho: ρ = 0 ; Ha: ρ ≠ 0

Test statistic :  t = r*√(n-2)/√(1-r²) = 0.361*√(11-2)/√(1-0.361²) = 1.16

df = n-2 = 9

p-value = T.DIST.2T(1.16, 9) = 0.275

Decision: p-value > 0.05 , Fail to reject the null hypothesis.

There is no correlation between age and weight.