Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information.
x | 0.338 | 0.310 | 0.340 | 0.248 | 0.367 | 0.269 |
y | 3.5 | 7.4 | 4.0 | 8.6 | 3.1 | 11.1 |
(a) Find Σx, Σy, Σx2, Σy2, Σxy, and r. (Round r to three decimal places.)
Σx = | |
Σy = | |
Σx2 = | |
Σy2 = | |
Σxy = | |
r = |
(b) Use a 5% level of significance to test the claim that
ρ ≠ 0. (Round your answers to two decimal places.)
t = | |
critical t = |
Conclusion
Reject the null hypothesis, there is sufficient evidence that ρ differs from 0.Reject the null hypothesis, there is insufficient evidence that ρ differs from 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ differs from 0.Fail to reject the null hypothesis, there is sufficient evidence that ρ differs from 0.
(c) Find Se, a, and b. (Round
your answers to four decimal places.)
Se = | |
a = | |
b = |
(d) Find the predicted percentage ŷ of strikeouts for a
player with an x = 0.3 batting average. (Round your answer
to two decimal places.)
%
(e) Find an 80% confidence interval for y when x
= 0.3. (Round your answers to two decimal places.)
lower limit | % |
upper limit | % |
(f) Use a 5% level of significance to test the claim that
β ≠ 0. (Round your answers to two decimal places.)
t = | |
critical t = |
Conclusion
Reject the null hypothesis, there is sufficient evidence that β differs from 0.Reject the null hypothesis, there is insufficient evidence that β differs from 0. Fail to reject the null hypothesis, there is insufficient evidence that β differs from 0.Fail to reject the null hypothesis, there is sufficient evidence that β differs from 0.
Solution :
a) ∑X = 1.872
∑Y = 37.7
∑X^2 = 0.594498
∑Y2 = 289.79
∑X⋅Y = 11.0934
r = -0.900
b)
Let x be a random variable that represents the batting average of a professional baseball player....
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