Let x be a random variable that represents the percentage of successful free thr

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 67 70 69 81 65 86 y 51 54 45 56 50 49 Given that ?x = 438, ?y = 305, ?x2 = 32,332, ?y2 = 15,579, ?xy = 22,302, and r = 0.226, find the P-value for a test claiming that ? is greater than zero.

Explanation / Answer

Ho:corr coeff=0

H1:corr coeff>0

Perform corr test in R

x <- c(67, 70, 69 ,81, 65, 86 )
y <- c( 51 ,54, 45 ,56, 50 ,49)
cor.test(x,y,alternative ="greater")

output:

Pearson's product-moment correlation

data: x and y

t = 0.46412, df = 4, p-value = 0.3333

alternative hypothesis: true correlation is greater than 0

95 percent confidence interval:

-0.6166797 1.0000000

sample estimates:

cor

0.2260542

r=0.2260542

there exists a weak positive relationship between x and y

p-value = 0.3333

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