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, 64, 75, 86, 73, 73 y= 44, 39, 48, 51, 44, 51

x=438,y=277,x²=32264,y²=12899,xy=20365, andr0.803.

S_e3.1357,a9.918,b0.4966, andx73.000.S_e

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

=45.18%

(a) Find a 90% confidence interval forywhenx=71. (Round your answers to one decimal

place.)

lower limit%=

upper limit%=

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

t=

critical t=

(c) Find a 90% confidence interval for. (Round your answers to three decimal places.)

lower limit=

upper limit=