Question: Is there a significant correlation between the Field Goal% and Free Throw % of NBA players? Data was collected from a random sample of 180

Is there a significant correlation between the Field Goal% and Free Throw % of NBA players? Data was collected from a random sample of 180 NBA players. The sample correlation coefficient between Field Goal % and Free Throw % was calculated to be -0.3576. Testing the null hypothesis that there is no correlation between these two variables, what is the value of the observed t statistic? Using the same NBA data described in Question 1, a simple linear regression model was fit with Free Throw % as the response variable and Field Goal % as the explanatory variable. The coefficient estimates and their associated standard errors are displayed in the table below. Based on the output, what is the 95% confidence interval estimate of the population slope \beta_1?

Coefficients Standard Error
Intercept 1.0606 0.0584
Field Goal % -0.6578 0.1280

A new recruit to the NBA has a Field Goal % of 0.506. Using the output in Question 2, what is a 95% prediction interval of this player's Free Throw%?

(Note the sample mean of the variable Field Goal % is 0.4531 and the sample standard deviation is 0.0535. The standard error of the estimate of the simple linear regression model is S_\epsilon=0.0922).

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