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 25 26.75 27.5 26.5 Head Circumference​ (inches), y 17.5 16.9 17.3 17.5 17.3

​(a) Use technology to determine

s Subscript b 1sb1.

equals=nothing  

(b) Test whether a linear relation exists between height and head circumference at the

alphaαequals=0.010.01

level of significance. State the null and alternative hypotheses for this test.

Choose the correct answer below.

A.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0not equals≠0

B.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1not equals≠0

C.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0greater than>0

D.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1greater than>0

Determine the​ P-value for this hypothesis test.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

What is the conclusion that can be​ drawn?

A.

Do not rejectDo not reject

Upper H 0H0

and conclude that a linear relation

does not existdoes not exist

between a​ child's height and head circumference at the level of significance

alphaαequals=0.01

B.

RejectReject

Upper H 0H0

and conclude that a linear relation

existsexists

between a​ child's height and head circumference at the level of significance

alphaαequals=0.01

C.

RejectReject

Upper H 0H0

and conclude that a linear relation

does not existdoes not exist

between a​ child's height and head circumference at the level of significance

alphaαequals=0.010.01.

D.

Do not rejectDo not reject

Upper H 0H0

and conclude that a linear relation

existsexists

between a​ child's height and head circumference at the level of significance

alphaαequals=0.01

Answer 1

The statistical software output for this problem is:

Hence,

a) sb1 = 0.0333

b) Hypotheses: Option B is correct.

P-value = 0.005

Conclusion: Option B is correct.