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   Head Circumference_(inches)_-_y
26.5   17.3
27.5   17.5
27.75   17.6
25   16.9
25.5   17.1

​(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 αe=0.01level of significance. State the null and alternative hypotheses for this test.

Choose the correct answer below.

A.

H0​: β0=0

H1​: β0>0

B.

H0​: β0=0

H1​: β0≠0

C.

H0​: β1=0

H1​: β1>0

D.

H0​: β1=0

H1​: β1≠0

Determine the​ P-value for this hypothesis test.

​P-value=__?__

​(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​ child's height and head circumference at the level of significance α=0.01.

B.

Reject H0 and conclude that a linear relation does not existbetween a​ child's height and head circumference at the level of significance α=0.01.

C.

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

D.

Do not reject H0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance α=0.01.

Answer 1

The excel output for the given data is:

Hence,

a) sb1 = Standard error of slope = 0.0159

b) Hypotheses:

H0​: β1=0

H1​: β1≠0

Option D is correct.

P - value = 0.001

Conclusion: Reject H0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance α=0.01.

Option C is correct.