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 α=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)230 15.8264 15.6359 15.5482 15.3531 14.9What are the null and alternative​ hypotheses?

Accepted Solution

Answer:YesNoStep-by-step explanation:The data is as follows;X       Y X*Y         X*X         Y*Y230      15.9 3657 52900 252.81265      15.7 4160.5 70225 246.49358      15.4 5513.2 128164 237.16480      15.3 7344 230400 234.09530      14.9 7897 280900 222.01∑X = 1863 ∑Y = 77.2 ∑X² =762589   ∑Y² = 28571.7  ∑XY = 1192.56The correlation coefficient is gives as follows;[tex]r= \frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{n\sum X^{2}-\left (\sum X}^{2} \right )\cdot \sqrt{n\sum Y^{2}-\left (\sum Y}^{2} \right )}[/tex]Where n = 5, plugging in the values, we have r= -0.95896We now find the test statistic s follows[tex]t = \frac{r}{\sqrt{\frac{1-r^2}{n-2} } }[/tex] plugging in the values gives t = -5.858With df = 3, we have the probability given as p = 0.00496 which is lesser than α = 0.05 we therefore reject the null hypothesis therefore, yes there is correlation between lemon imports and crash fatalities.No, because lemon imports and car fatalities only correlate, the cause of car fatalities will be found at the point the crash occurs.