Question

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.

x	65	80	68	64	69	71
y	43	49	51	47	42	52

Given that S_e ≈ 4.306, a ≈ 17.085, b ≈ 0.417, and , ∑x = 417, ∑y = 284, ∑x² = 29,147, and ∑y² = 13,528, find a 98% confidence interval for y around 53.4 when x = 87.

between 24.6 and 79.1

between 21.3 and 82.5

between 25.1 and 78.6

between 26.4 and 77.3

between 23.8 and 79.9

Answer 1

Given:

The random sample of n = 6 professional basketball players gave the following information.

x	65	80	68	64	69	71
y	43	49	51	47	42	52

Given that Se ≈ 4.306, a ≈ 17.085, b ≈ 0.417, and , ∑x = 417, ∑y = 284, ∑x2 = 29,147, and ∑y2 = 13,528,

The regression line equation is given by

Therefore a 98% confidence interval for y around 53.4 when x = 87 is between 37.3 and 69.5 (option not given)