Letxbe a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Letybe a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample ofn= 6 professional basketball players gave the following information.x676475867373y443948514451

(a) Verify thatx=438,y=277,x²=32264,y²=12899,xy=20365, andr0.803.xyx²y²xyr

(b) Use a 5% level of significance to test the claim that> 0. (Round your answers to two decimal places.)tcriticaltConclusion

Reject the null hypothesis, there is sufficient evidence that> 0.

Reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is sufficient evidence that> 0.

(c) Verify thatS_e3.1357,a9.918,b0.4966, andx73.000.S_eabx

(d) Find the predicted percentageof successful field goals for a player withx=67%successful free throws. (Round your answer to two decimal places.)

%

(e) Find a 90% confidence interval forywhenx=67. (Round your answers to one decimal place.)lower limit%upper limit%

(f) Use a 5% level of significance to test the claim that> 0. (Round your answers to two decimal places.)tcriticaltConclusion

Reject the null hypothesis, there is sufficient evidence that> 0.

Reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is sufficient evidence that> 0.

(g) Find a 90% confidence interval for. (Round your answers to three decimal places.)lower limitupper limit

Interpret its meaning.

For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval.

For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval.

For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval.

For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval.