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	73	74	80	66	77	77
y	50	52	45	46	52	53

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Verify that S_e ≈ 3.694, a ≈ 38.254, b ≈ 0.153, and , ∑x =447, ∑y =298, ∑x² =33,419, and ∑y² =14,858, and use a 5% level of significance to find the P-value for the test that claims that β is greater than zero.

Group of answer choices

A) Since the P-value is greater than α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

B) Since the P-value is less than α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

C) Since the P-value is equal to α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

D) Since the P-value is equal to α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

E) Since the P-value is greater than α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.

Answer 1

I am using Excel the command is Data> Data Analysis >Regression > select the data > ok

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SUMMARY OUTPUT
Regression Statistics
Multiple R	0.2193
R Square	0.0481
Adjusted R Square	-0.1899
Standard Error	3.6938
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.7574	2.7574	0.2021	0.6763
Residual	4	54.5759	13.6440
Total	5	57.3333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	38.2539	25.4315	1.5042	0.2070	-32.3554	108.863161
x	0.1532	0.3408	0.4496	0.6763	-0.7929	1.099299156

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P-value = 0.6763/2 = 0.3361

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E) Since the P-value is greater than α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero.