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 (x=0.05.

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_(x)   Crash_Fatality_Rate_(y)
228   15.8
265   15.6
358   15.5
480   15.3
530   14.9

Construct a scatterplot.

The linear correlation coefficient r is

Answer 1

	X	Y	X * Y	X2	Y2
	228	15.8	3602.4	51984	249.64
	265	15.6	4134	70225	243.36
	358	15.5	5549	128164	240.25
	480	15.3	7344	230400	234.09
	530	14.9	7897	280900	222.01
Total	1861	77.1	28526.4	761673	1189.35

r = - 0.9472

To Test :-

H0 :- ρ = 0
H1 :- ρ ≠ 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( -0.9472 * √(5 - 2) ) / (√(1 - 0.8972) )
t = -5.1169

Test Criteria :-
Reject null hypothesis if t < -t(α,n-2)
t(α/2,n-2) = t(0.05/2 , 5 - 2 ) = 3.1824
t < -t(α/2, n-2) = -5.1169 < -3.1824
Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 5.1169 ) = 0.0144
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0144 < 0.05 ,hence we reject null hypothesis
Conclusion :- We reject H0

There is sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality​ rates.