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: 81 65 78 87 70 81 y: 46 48 54 51 44 51 Given that Se ≈ 3.668, a ≈ 16.331, b ≈ 0.436, and x-bar ≈ 77, use a 5% level of significance to find the P-Value for the test that claims β is greater than zero. ​ Select one:​ a. 0.005 < P-Value < 0.01 b. P-Value > 0.25 c. 0.1 < P-Value < 0.2 d. 0.2 < P-Value < 0.25 e. P-Value < 0.005

Answer 1

The statistical software output for this problem is:

Simple linear regression results:

Dependent Variable: y
Independent Variable: x
y = 32.93865 + 0.20858896 x
Sample size: 6
R (correlation coefficient) = 0.4567154
R-sq = 0.20858896
Estimate of error standard deviation: 3.6679678

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	32.93865	15.714057	≠ 0	4	2.0961265	0.1041
Slope	0.20858896	0.20314995	> 0	4	1.0267734	0.1813

Hence,

0.1 < P-Value < 0.2

Option C is correct.