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 theP-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
A:
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.