Question

Do larger butterflies live longer? The wingspan, in millimeters, and the lifespan in the adult state, in days, were measured for 22 species of butterfly. The results of the test of the null hypothesis \rho=0ρ=0is shown below, and we'll use a level of significance of 0.05.

LinRegTTest

y= a+bx

\beta\ne0β​=0 and \rho\ne0ρ​=0

t =-2.8982844267

p=0.0090879947

df=20

a=57.35324963

b= -1.049298322

s=6.312461676

r²=0.2957759297

r= -0.6443528566

Answer each question below - for all numerical answers, round to 3 decimal places

The line of best fit is y = (blank )+(Blank)x . The predicted lifespan of a butterfly with a wingspan of 30 millimeters isQuestion Blankdays. Can we conclude that larger butterflies live longer than smaller butterflies?Question Blank.Because the correlation coefficient isQuestion Blankwhich means there is a (negative or positive)Question Blankcorrelation between size. And the p-value ofQuestion Blankshows that the test (is or is not)Question Blanksignificant at the 0.05 level. Therefore as size increases, lifespan (increases or decreases)Question Blank.

Answer 1

Solution :

The line of best fit is

$\hat y= 57.353-1.049*x$

To predict the lifespan of butterfly with a wingspan (x)= 30 is

$\hat y= 57.353-1.049*30$

9 = 57.353 - 31.47

$\hat y= 25.883$

we can not conclude that larger butterflies live longer than smaller because the correlation coefficient is r=-0.644.

which means that there is negative correlation between sizes and P value 0.009 shows that the test is significant at the 0.05 level. Threfore as size increases lifespan decreases