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.

x0.3100.2980.3400.2480.3670.269y2.57.84.08.63.111.1

(a) Verify thatx=1.832,y=37.1,x²=0.569058,y²=289.87,xy=10.7158, andr-0.800.

xyx²y²xyr

(b) Use a10%level of significance to test the claim that?0. (Use 2 decimal places.)

tcriticalt

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) Verify thatS_e2.3343,a25.475, andb-63.182.S_eab

(d) Find the predicted percentageof strikeouts for a player with anx=0.33batting average. (Use 2 decimal places.)

%

(e) Find a90%confidence interval forywhenx=0.33. (Use 2 decimal places.)

lower limit%upper limit%

(f) Use a10%level of significance to test the claim that?0. (Use 2 decimal places.)

tcriticalt

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 a90%confidence interval for?and interpret its meaning. (Use 2 decimal places.)lower limitupper limit

Interpretation

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 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 within the confidence interval.