Question

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 S_e, 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.

Answer 1

Solution :

a) ∑X = 1.872

∑Y = 37.7

  ∑X^2 = 0.594498

∑Y2 = 289.79

  ∑X⋅Y = 11.0934

r = -0.900

b)