Question

Listed below are annual data for various years. The data are weights​ (metric tons) of imported lemons and car crash fatality rates per​ 100,000 population. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using alpha equals0.05 . Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality​ rates? Do the results suggest that imported lemons cause car​ fatalities? Lemon Imports 231 265 357 482 530 Crash Fatality Rate 15.9 15.7 15.4 15.2 14.8

Answer 1

We will use the R code to solve the problem :

We will define x= Lemon Imports

and y = Crash Fatality Rate

We will define the following terms as follows to calculate r = correlation coefficient​

Sxx = - n* (x_bar)²

Syy = - n* (y_bar)²

Sxy = - n*(x_bar)*(y_bar)

r = Sxy/(Sxx*Syy)^0.5

x_bar = / n

y_bar = /n

We have the following results

x_bar = 373

y_bar = 13.4

sxx = 68614

syy = 70.74

sxy = 1200.6

r= 1200.6/ (70.74*68614)^0.5

r  = 0.5449535

Not to test for linear correlation

Therefore Ho : = 0 vs H1  0

Therefore the test - statistics under Ho is as follows

t = r* _/ follows with n-2 degrees of freedom

t= 1.125731

p value = 0.342207

Conclusion : Since p value = 0.342207 > = 0.05 we do not have sufficient evidence to reject Ho . And we conclude that there is not sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality​ rates.