Letx be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Lety be 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
|
69 |
66 |
63 |
65 |
76 |
76 |
y
|
54 |
53 |
51 |
43 |
47 |
45 |
Verify thatSe
≈ 4.739,a ≈ 67.050,b≈ –0.263, and , ∑x =415, ∑y =293, ∑x2 =28,863, and ∑y2 =14,409, and find a 90% confidence interval forβ and interpret its meaning. Round your final answers to three decimal places.
answer choices:
The 90% confidence interval forβ is from –0.993 to 0.466 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.99 and 0.47.
The 90% confidence interval forβ is from –1.065 to 0.539 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.07 and 0.54.
The 90% confidence interval forβ is from –0.882 to 0.355 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –0.88 and 0.36.
The 90% confidence interval forβ is from –1.023 to 0.496 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.02 and 0.50.
The 90% confidence interval forβ is from –1.309 to 0.782 and means that for every percentage increase in successful free throws, there is 90% confidence that the percentage of successful field goals increases by an amount between –1.31 and 0.78.