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

alphaαequals=0.050.05.

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	228228	266266	357357	483483	532532
Crash Fatality Rate	15.915.9	15.615.6	15.515.5	15.215.2	14.814.8

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρless than<0

B.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρnot equals≠0

C.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρgreater than>0

D.

Upper H 0H0​:

rhoρnot equals≠0

Upper H 1H1​:

rhoρequals=0

Construct a scatterplot. Choose the correct graph below.

A.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 15.9); (270, 15.6); (360, 15.5); (480, 15.2); (530, 14.8). All horizontal coordinates are approximate.

B.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (200, 14.9); (230, 15.9); (330, 16.2); (400, 15.1); (560, 15.3). All horizontal coordinates are approximate.

C.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 15.9); (270, 15.6); (360, 15.5); (480, 15.6); (530, 15.9). All horizontal coordinates are approximate.

D.

020040060014151617xy

A scatterplot has a horizontal x-scale from 0 to 600 in increments of 100 and a vertical y-scale from 14 to 17 in increments of 0.5. Five points are plotted with coordinates as follows: (230, 14.8); (270, 15.2); (360, 15.5); (480, 15.6); (530, 15.9). All horizontal coordinates are approximate.The linear correlation coefficient r is

nothing.

Answer 1

Interpretation:

The scatter plot of the variables lemon imports (X) and the car fatalities (Y) indicates that the strong negative linear relationship. Since, the direction of the data points is down wards. Hence, we can say that there is negative linear relationship between the variables. The main conclusion of the part (a) and the interpretation of the scatter plot are the same.