Letxbe a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Letybe a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample ofn= 6 professional basketball players gave the following information.x676475867373y424048514451

(a) Verify thatx=438,y=276,x²=32264,y²=12806,xy=20295, andr0.823.

x

y

x²

y²

xy

r

(b) Use a 5% level of significance to test the claim that> 0. (Round your answers to two decimal places.)tcriticaltConclusion

Reject the null hypothesis, there is sufficient evidence that> 0.

Reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is sufficient evidence that> 0.

(c) Verify thatS_e2.9785,a8.997,b0.5069, andx73.000.S_eabx

(d) Find the predicted percentageof successful field goals for a player withx=81%successful free throws. (Round your answer to two decimal places.)

%

(e) Find a 90% confidence interval forywhenx=81. (Round your answers to one decimal place.)lower limit%upper limit%

(f) Use a 5% level of significance to test the claim that> 0. (Round your answers to two decimal places.)

t

criticalt

Conclusion

Reject the null hypothesis, there is sufficient evidence that> 0.

Reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is insufficient evidence that> 0.

Fail to reject the null hypothesis, there is sufficient evidence that> 0.

(g) Find a 90% confidence interval for. (Round your answers to three decimal places.)

lower limit

upper limit

Interpret its meaning.

For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls within the confidence interval.

For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls outside the confidence interval.

For every percentage increase in successful free throws, the percentage of successful field goals increases by an amount that falls outside the confidence interval.

For every percentage increase in successful free throws, the percentage of successful field goals decreases by an amount that falls within the confidence interval.

10.

[-/5.34 Points]

DETAILS

BBUNDERSTAT12 9.3.008.

MY NOTES

ASK YOUR TEACHER

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.x0.3360.2760.3400.2480.3670.269y2.87.14.08.63.111.1

(a) Verify thatx=1.836,y=36.7,x²=0.573226,y²=281.03,xy=10.5168, andr-0.888.

x

y

x²

y²

xy

r

(b) Use a10%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_e1.7280,a25.249, andb-62.524.S_eab

(d) Find the predicted percentageof strikeouts for a player with anx=0.294batting average. (Use 2 decimal places.)

%

(e) Find a99%confidence interval forywhenx=0.294. (Use 2 decimal places.)

lower limit%

upper limit%

(f) Use a10%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.

(g) Find a99%confidence interval forand 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 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 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.