Question

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x	67	64	75	86	73	73
y	44	40	48	51	44	51

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

t =
critical t =

Conclusion

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

(c) Find S_e, a, b, and x. (Round your answers to four decimal places.)

Se =
a =
b =
x =

(d) Find the predicted percentage ŷ of successful field goals for a player with x = 80% successful free throws. (Round your answer to two decimal places.)
%

(e) Find a 90% confidence interval for y when x = 80. (Round your answers to one decimal place.)

lower limit	%
upper limit	%

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

t =
critical t =

Conclusion

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

Answer 1

b)

test statistic t =		r*(√(n-2)/(1-r2))=		2.700
t crit =				2.13

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

c)

Se =√(SSE/(n-2))=				2.93630
a=				12.3506
b=				0.4655
X̅=				73.0000

d)

predicted value =

49.59

e)

std error of confidence interval =				s*√(1+1/n+(x0-x̅)2/Sxx)=			3.3935
for 90 % confidence and 4degree of freedom critical t=							2.132
lower limit =		42.4
uppr limit =		56.8

f)

test statistic t =		r*(√(n-2)/(1-r2))=		2.700
t crit =				2.13

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