Letxbe a random variable that represents the batting average of a professional baseball player. Letybe a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample ofn= 6 professional baseball players gave the following information.x0.3120.2800.3400.2480.3670.269y2.77.84.08.63.111.1

(a) Verify thatx=1.816,y=37.3,x²=0.559898,y²=290.91,xy=10.6428, andr-0.831.xyx²y²xyr

(b) Use a5%level of significance to test the claim that0. (Use 2 decimal places.)t

criticalt

Conclusion

Reject the null hypothesis, there is sufficient evidence thatdiffers from 0.

Reject the null hypothesis, there is insufficient evidence thatdiffers from 0.

Fail to reject the null hypothesis, there is insufficient evidence thatdiffers from 0.

Fail to reject the null hypothesis, there is sufficient evidence thatdiffers from 0.

(c) Verify thatS_e2.1361,a25.302, andb-63.057.S_eab

(d) Find the predicted percentageof strikeouts for a player with anx=0.34batting average. (Use 2 decimal places.)

%

(e) Find a95%confidence interval forywhenx=0.34. (Use 2 decimal places.)lower limit

%upper limit

%

(f) Use a5%level of significance to test the claim that0. (Use 2 decimal places.)tcriticaltConclusion

Reject the null hypothesis, there is sufficient evidence thatdiffers from 0.

Reject the null hypothesis, there is insufficient evidence thatdiffers from 0.

Fail to reject the null hypothesis, there is insufficient evidence thatdiffers from 0.

Fail to reject the null hypothesis, there is sufficient evidence thatdiffers from 0.

(g) Find a95%confidence interval forand interpret its meaning. (Use 2 decimal places.)lower limitupper limitInterpretation

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.