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 alphaequals0.05. 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 231 264 357 482 531 Crash Fatality Rate 15.9 15.6 15.5 15.2 14.9

Answer 1

Let X: Lemon import data and Y: Crash Fatality Rate

Construct scatter plot:

Now, we have to construct below table using given data, we get

	X	Y	X2	Y2	XY
	231	15.9	53361	252.81	3672.9
	264	15.6	69696	243.36	4118.4
	357	15.5	127449	240.25	5533.5
	482	15.2	232324	231.04	7326.4
	531	14.9	281961	222.01	7911.9
Total	1865	77.1	764791	1189.47	28563.1

We have to find correlation coefficient (r) using above table values, we get

  

Now we have to find test statistic value:

P value for t = -6.91 and alpha = 0.05, is 0.0062

Since alpha = 0.05 > p = 0.0062, we reject the null hypothesis (i.e. ) and conclude that there is a linear correlation between lemon imports and crash fatality​ rates