A company would like to examine the linear relationship betw

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 0.977. Using this data and a = 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 39 27 56 24 32 Credit score 670 650 755 615 660 What are the correct null and alternative hypotheses? H0:p>0 H1:p = 0 H0 :p 0 H1 :p = 0 H0: p = 0 H1:p 0 H0: p = 0 H1:p>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. zero. enough evidence from the sample to conclude that p is H0. There

Solution

a)

Here,

Ho: rho = 0
Ha: rho =/= 0 [ANSWER, B]

******************************

b)

Using technology, we get the correlation,              
              
r =    0.976621359          

              
As t = r sqrt [(n - 2) / (1 - r^2)], then, as n = 5,              
              
t =    7.868926229 = 7.87   [ANSWER]

***************************      

c)
              

df =    3          
              
Then, by table/technology, as this is two tailed,

Pvalue = 0.004275962 [ANSWER]

**************************

d)

As P < 0.05,
              
REJECT Ho. There IS enough evidence from the sample to conclude that rho is NOT EQUAL to zero. [CONCLUSION]