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

Parts (a) and (b) relate to testing p. Part (c) requests the value of Se. Part (e) relates to confidence intervals for prediction. Part (f) relates to testing β.
Answers may vary due to rounding.
(a) Verify that ˆ‘x = 439, ˆ‘y = 280, ˆ‘x2 = 32,393, ˆ‘y2 = 13,142, ˆ‘xy = 20,599, and r ‰ˆ 0.784.
(b) Use a 5% level of significance to test the claim that p > 0.
(c) Verify that Se ‰ˆ 2.6964, a ‰ˆ 16.542, and b ‰ˆ 0.4117.
(d) Find the predicted percentage Å· of successful field goals for a player with x = 70% successful free throws.
(e) Find a 90% confidence interval for y when x = 70.
(f) Use a 5% level of significance to test the claim that β > 0.

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