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 alpha (Ī±) =0.05 Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Select all TRUE statements for the above hypothesis test from those given below.

Lemon_Imports_(x) Crash_Fatality_Rate_(y)
230 15.8
264 15.6
359 15.5
482 15.3
531 14.9

Reqiured:
a. What are the null and alternative​ hypotheses?
b. Construct a scatterplot.
c. The linear correlation coefficient r is: ________
d. The test statistic t is :__________
e. The​ P-value is :___________

Answer 1

Answer:

R = - 0.9453

T = - 5.019

Pvalue = 0.212

Step-by-step explanation:

Given the data:

Lemon_Imports_(x)

230

264

359

482

531

Crash_Fatality_Rate_(y):

15.8

15.6

15.5

15.3

14.9

The Correlation Coefficient, R using a correlation Coefficient calculator is - 0.9453 ; this depicts a strong negative correlation between the dependent and independent variable.

The test statistic, T :

T = r / √(1 - r²) / (n - 2)

T = -0.9453/ √(1 - (-0.9453)²) / (5 - 2)

T = - 0.9453 / 0.1883329

T = - 5.019

The Pvalue using a Pearson Pvalue calculator ;

df = n - 1 = 5 - 2 = 3 ; r = - 0.9453

Pvalue = 0.212