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.

x 67 65 75 86 73 73

y 42 40 48 51 44 51

(a) Verify thatx=439,y=276,x²=32393,y²=12806,xy=20335, andr0.814.

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

t=

criticalt=

Conclusion

(c) Verify thatS_e3.0468,a8.188,b0.5168, andx73.167.

(d) Find the predicted percentageof successful field goals for a player withx=71%successful free throws. (Round your answer to two decimal places.)

%

e) Find a 90% confidence interval forywhenx=71. (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.)

t

criticalt

Conclusion

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