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

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 βis greater than zero.

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 βis greater than zero.

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.

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 βis greater than zero.

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 βis greater than zero.

Answer 1

null hypothesis: Ho:               β1		=	0
Alternate Hypothesis: Ha: β1		>	0
0.05 level,right tail test and n-2= df, critical t=			2.132
Decision rule: reject Ho if test statistic t>2.132
estimated std error of slope =se(β1) =s/√Sxx=			0.3408
test stat t =	(bo-β1)/se(β1)=	=	0.4496
p value:		=	0.3382

since p value is rgeater than 0.05:

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.