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 0.330 0.270 0.340 0.248 0.367 0.269

y 3.1 7.5 4.0 8.6 3.1 11.1

Σx = 1.824, Σy = 37.4, Σx² = 0.565954, Σy² = 288.64, Σxy = 10.6644, and r ≈ -0.884.

(b) Use a 1% level of significance to test the claim that ? ≠ 0. (Use 2 decimal places.)

t

critical t ±

Conclusion?
Reject the null hypothesis, there is sufficient evidence that ? differs from 0.

Reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence that ? differs from 0.

(c) S_e ≈ 1.7400, a ≈ 24.943, and b ≈ -61.547.

(d) Find the predicted percentage  of strikeouts for a player with an x = 0.334 batting average. (Use 2 decimal places.)

(e) Find a 95% confidence interval for y when x = 0.334. (Use 2 decimal places.)

lower limit %

upper limit %

(f) Use a 1% level of significance to test the claim that ? ≠ 0. (Use 2 decimal places.)

t

critical t ±

Conclusion?
Reject the null hypothesis, there is sufficient evidence that ? differs from 0.

Reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence that ? differs from 0.

(g) Find a 95% confidence interval for ? 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 increases 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 outside the confidence interval.

For every unit increase in batting average, the percentage strikeouts decreases by an amount that falls within 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	0.330	0.270	0.340	0.248	0.367	0.269
y	3.1	7.5	4.0	8.6	3.1	11.1

Σx = 1.824, Σy = 37.4, Σx² = 0.565954, Σy² = 288.64, Σxy = 10.6644, and r ≈ -0.884.

(b) Use a 1% level of significance to test the claim that ? ≠ 0. (Use 2 decimal places.)

t
critical t ±

Conclusion?

Reject the null hypothesis, there is sufficient evidence that ? differs from 0.

Reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence that ? differs from 0.

(c) S_e ≈ 1.7400, a ≈ 24.943, and b ≈ -61.547.

(d) Find the predicted percentage of strikeouts for a player with an x = 0.334 batting average. (Use 2 decimal places.)

(e) Find a 95% confidence interval for y when x = 0.334. (Use 2 decimal places.)

lower limit	%
upper limit	%

(f) Use a 1% level of significance to test the claim that ? ≠ 0. (Use 2 decimal places.)

t
critical t ±

Conclusion?

Reject the null hypothesis, there is sufficient evidence that ? differs from 0.

Reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that ? differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence that ? differs from 0.

(g) Find a 95% confidence interval for ? 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 increases 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 outside the confidence interval.

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

Accepted Answer

Dear student, We are allowed three subparts , Please ask the remaining part separately

x
y…

x	y	xy	x²	y²
0.33	3.1	1.023	0.1089	9.61
0.27	7.5	2.025	0.0729	56.25
0.34	4	1.36	0.1156	16
0.248	8.6	2.1328	0.061504	73.96
0.367	3.1	1.1377	0.134689	9.61
0.269	11.1	2.9859	0.072361	123.21
1.824	37.4	10.6644	0.565954	288.64	Total