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.

Height_(inches)_-_x   Head Circumference_(inches)_-_y
26   17.3
24.5   17.1
27.75   17.6
26.5   17.3
27   17.5

(a) Treating height as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

β0≈=b0=13.2857​

(Round to four decimal places as​ needed.)

β1≈b1=0.1546

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

Se=0.0570

(Round to four decimal places as​ needed.)

​(c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine sb1.

sb1=0.0234  

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

(d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between height and head circumference at the α=0.01level of significance. State the null and alternative hypotheses for this test.

Choose the correct answer below.

D. H0​: β1=0 H1​: β1≠0

Determine the​ P-value for this hypothesis test.

​P-value=0.007

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

What is the conclusion that can be​ drawn?

A.

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 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

You did correct from a) to d)

Here we test H0 : 1 = 0 vs H1 : 1 0

From calculations we get p value = 0.007

Also = 0.01

Decision rule : If p-value    , we reject the null hypothesis H0 , otherwise we fail to reject the null hypothesis H0.

our p-value =0.007 < 0.01 , so we reject null hypothesis H0

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 A) is correct.