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?

Answer 1

Yes

No

Explanation:

The data is as follows;

X Y X*Y X*X Y*Y

230 15.9 3657 52900 252.81

265 15.7 4160.5 70225 246.49

358 15.4 5513.2 128164 237.16

480 15.3 7344 230400 234.09

530 14.9 7897 280900 222.01

∑X = 1863 ∑Y = 77.2 ∑X² =762589 ∑Y² = 28571.7 ∑XY = 1192.56

The correlation coefficient is gives as follows;

`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 )}`

Where n = 5, plugging in the values, we have r= -0.95896

We now find the test statistic s follows

`t = \frac{r}{\sqrt{(1-r^2)/(n-2) } }` plugging in the values gives t = -5.858

With 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.