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 0.314 0.280 0.340 0.248 0.367 0.269 y 3.2 7.4 4.0 8.6 3.1 11.1 (a) Verify that Σx = 1.818, Σy = 37.4, Σx2 = 0.56115, Σy2 = 287.78, Σxy = 10.6932, and r ≈ -0.852. Σx Σy Σx2 Σy2 Σxy r (b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 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) Verify that Se ≈ 1.9362, a ≈ 25.038, and b ≈ -62.063. Se a b (d) Find the predicted percentage of strikeouts for a player with an x = 0.312 batting average. (Use 2 decimal places.) %(e) Find a 95% confidence interval for y when x = 0.312. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 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. (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit Interpretation For every unit increase in batting average, the percentage strikeouts increases by an amount that falls within the confidence interval.For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval. For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls within the confidence interval.For every unit increase in batting average, the percentage strikeouts increases by an amount that falls outside the confidence interval.

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	0.314	0.280	0.340	0.248	0.367	0.269
y	3.2	7.4	4.0	8.6	3.1	11.1

(a) Verify that Σx = 1.818, Σy = 37.4, Σx² = 0.56115, Σy² = 287.78, Σxy = 10.6932, and r ≈ -0.852.

Σx
Σy
Σx²
Σy²
Σxy
r

(b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 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) Verify that S_e ≈ 1.9362, a ≈ 25.038, and b ≈ -62.063.

S_e
a
b

(d) Find the predicted percentage of strikeouts for a player with an x = 0.312 batting average. (Use 2 decimal places.)
%

(e) Find a 95% confidence interval for y when x = 0.312. (Use 2 decimal places.)

lower limit	%
upper limit	%

(f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 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.

(g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.)

lower limit
upper limit

Interpretation

For every unit increase in batting average, the percentage strikeouts increases by an amount that falls within the confidence interval.For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls outside the confidence interval. For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls within the confidence interval.For every unit increase in batting average, the percentage strikeouts increases by an amount that falls outside the confidence interval.