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	26	27.75	25.5	27.5	24.5
Head Circumference​ (inches), y	17.3	17.6	17.1	17.5	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 a=0.01 level 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​: β1=0

H1​:β1>0

C. H0​:β0=0

H1​:β0≠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 exist between a​ child's height and head circumference at the level of significance α=0.01

C. 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

D.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

Answer 1

The statistical software output for this problem is:

Hence,

a) sb1 = 0.0267

b) H0​:β0=0

H1​:β0≠0

Option C is correct.

p - Value = 0.009

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. Option D is correct.