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 61 67 75 86 73 73

y 40 39 48 51 44 51

(b) Use a 5% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t critical t

(d) Find the predicted percentage y hat of successful field goals for a player with x = 71% successful free throws. (Use 2 decimal places.) %

(e) Find a 99% confidence interval for y when x = 71. (Use 1 decimal place.) lower limit % upper limit %

(f) Use a 5% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t

(g) Find a 99% confidence interval for β and interpret its meaning. (Use 3 decimal places.) lower limit upper limit

Answer 1

b)

test statistic t =		r*(√(n-2)/(1-r2))=		2.80
t crit =				2.13

d)

predicted value =

0.5164*71+8.0640 =

44.73

e)

std error of confidence interval =				s*√(1+1/n+(x0-x̅)2/Sxx)=			3.7433
for 99 % confidence and 4degree of freedom critical t=							4.604
lower limit =		27.5
uppr limit =		62.0

f)

test statistic t =		r*(√(n-2)/(1-r2))=		2.80
t crit =				2.13

g)

std error of slope sb1 =				s/√SSx=		0.1843
for 99 % confidence and -2degree of freedom critical t=						4.6040
99% confidence interval =b1 -/+ t*standard error=					(-0.332,1.365)
lower limit =		-0.332
uppr limit =		1.365