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
27.75   17.6
27   17.5
27.5   17.5
25.5   17.1
25   16.9

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

C.

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.

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

Solution:

Go to Data >data analysis>regression you will get

Regression output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.98518
R Square	0.97058
Adjusted R Square	0.960774
Standard Error	0.060073
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.357174	0.357174	98.97252	0.002161
Residual	3	0.010826	0.003609
Total	4	0.368
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	10.86901	0.648995	16.74744	0.000464	8.803615	12.9344
Height_x	0.242975	0.024423	9.948493	0.002161	0.165249	0.320701

From Regression

Solution1:

​(a) Use technology to determine sb1.

sb1=__?__  standard error of slope=0.0244

Solution(B)

B.

H0​: β1=0

H1​: β1≠0

Determine the​ P-value for this hypothesis test.

P=0.002
P<0.01

Reject Ho.accept Ha,There is a linear relationship.

B.

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.