A company would like to examine the linear relationship between the age and cred

Question

A company would like to examine the linear relationship between the age and credit score of an individual. The following table shows the credit scores and ages of 5 randomly selected people. These data have a sample correlation coefficient, rounded to three decimal places, of 0.967. Using this data and alpha = 0 05, test if the population correlation coefficient between a person's age and credit score is different than zero. What conclusions can you draw? Age 32 28 52 20 36 Credit score 675 655 765 615 660 What are the correct null and alternative hypotheses? A. H_0: rho = 0 H_1: rho > 0 B. H_0: rho notequalto 0 H_1: rho = 0 C. H_0: rho = 0 H_1: rho notequalto 0 D. H_0: rho >0 H_1: rho = 0 What is the test statistic? t = (Round to two decimal places as needed.) What is the p-value? p-value = (Round to three decimal places as needed.) State the conclusion. H_0. There enough evidence from the sample to conclude that rho is zero.

Explanation / Answer

Solution:

Here,
test hypothesis
A) Ho: p = 0
H1: p 0

here, we have correlation,
r = 0.967   

  
As t = r sqrt [(n - 2) / (1 - r^2)], then, as n = 5,
= 0.967 *sqrt((5-2)/(1-0.967^2)
  
t = 6.57397354 = 6.57

df = 4
  
Then, by table/technology, as this is two tailed,

P-value = 0.0028

As P < 0.05,
  
Reject Ho. There is enough evidence from the sample to conclude that p is NOT EQUAL to zero.

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