Question

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x	64	64	88	66	64	72
y	38	45	50	45	45	41

Given that ∑x = 418, ∑y = 264, ∑x² = 29,572, ∑y² = 11,700, ∑xy = 18,514, and r = 0.627, find the critical value for a test using a 2.5% level of significance claiming that ρ is greater than zero.

Select one:

a. 0.727

b. 0.741

c. 6.869

d. 4.604

e. 2.776

Answer 1

Ans. The correct option is (e), i.e., the critical value is 2.776

The theoretical population coefficient of correlation , which estimated by the sample correlation coefficient ''. To test this t-statistic is used.

       

r: sample coefficient of correlation (r= 0.627, given in the question)

N: sample size (N=6)

degree of freedom(df)= N-2 , for this t-statistic

We have to check the claim that , so are Null and Alternate hypothesis are:

Now the t-statistic,   

the critical value for , is ,