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 69 66 63 65 76 76 y 54 53 51 43 47 45 Verify that Se ≈ 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 for β and interpret its meaning. Round your final answers to three decimal places. answer choices: The 90% confidence interval for β 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 for β 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 for β 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 for β 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 for β 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.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...

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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	69	66	63	65	76	76
y	54	53	51	43	47	45

Verify that S_e ≈ 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 for β and interpret its meaning. Round your final answers to three decimal places.

answer choices:

The 90% confidence interval for β 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 for β 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 for β 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 for β 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 for β 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.

Expert Solution

Step 1

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.

n=6

The excel steps for regression is obtained as-

The steps taken to obtain the simple linear regression to determine the amount of time spent on homework can be predicted by amount of sleep is given as follows: -

Enter the data in Excel spreadsheet [ x and y]
Go to data>Go to data analysis>Select regression>click OK.
Select Input Y Range>Select Input X Range>click Labels>click Ok

The output obtained is given as follows-

Regression Statistics
Multiple R	0.331
R Square	0.109
Adjusted R Square	-0.113
Standard Error	4.739
Observations	6

ANOVA
	df	SS	MS	F	Significance F
Regression	1	11.01801329	11.018013	0.490696	0.522220859
Residual	4	89.81532004	22.45383
Total	5	100.8333333

	Coefficients	Standard Error	t Stat	P-value	Lower 90.0%	Upper 90.0%
Intercept	67.050	26.078	2.571	0.062	11.457	122.644
x	-0.263	0.376	-0.700	0.522	-1.065	0.539

The table below shows the required calculation-

	x	y	x2	y2
	69	54	4761	2916
	66	53	4356	2809
	63	51	3969	2601
	65	43	4225	1849
	76	47	5776	2209
	76	45	5776	2025
Total	415	293	28863	14409

Thus,

$s_{e} \approx 4.739 a \approx 67.050 b \approx - 0.263 \sum_{i} x = 415 \sum_{j} y = 293 \sum_{i} x^{2} = 28863 \sum_{j} y^{2} = 14409$

is verified.

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