Question

A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts (a) and (b) below.

Height (inches), x	27 24.5 27.75 26.5 27.5
Head Circumference (inches), y	17.5 17.1 17.6 17.3 17.5

(a) Use technology to determine sb1

sb1= ______

(Round to four decimal places as needed)

(b) Test whether a linear relation exists between height and head circumference at the a=0.10 level of significance. State the null and alternative hypotheses for this test.

A) H0: B1=0

H1: B1 =/ (not equal) 0

B) H0: B0=0

H1: B0>0

C) H0:B0=0

H1: B0 =/ (not equal) 0

D) H0: B1=0

H1: B1 > 0

Determine the P-value for this hypothesis test.

P-value is ______ (Round to three decimal places as needed)

What is the conclusion that can be drawn?

A) Do not reject H0 and conclude that a linear relation exists between a childs height and head circumference at the level of significance a=0.01

B) Reject H0 and conclude that a linear relation exists between a childs height and head circumference at the level of significance a=0.01

C) Reject H0 and conclude that a linear relation does not exist between a childs height and head circumference at the level of significance a=0.01

D) Do not reject H0 and conclude that a linear relation does not exist between a childs height and head circumference at the level of significance a=0.01

Answer 1

SSE =Syy-(Sxy)2/Sxx=

0.011

	s2 =SSE/(n-2)=	0.0036
std error σ              =	=se =√s2=	0.060

a)

std error of slope =se(β1) =s/√Sxx=

0.0231

b)

option A is correct

null hypothesis: Ho:           β1=		0
Alternate Hypothesis: Ha: β1≠		0

test stat t =(b1-β1)/se(β1)=		6.455
p value =	0.008	(from excel:tdist(6.455,3,2)

B) Reject H0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance a=0.01