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 27.75 25 27 26 26.5 Head Circumference​ (inches), y 17.6 16.9 17.5 17.3 17.3 ​(a) Use technology to determine s Subscript b 1. s Subscript b 1equals nothing   ​(Round to four decimal places as​ needed.) ​(b) Test whether a linear relation exists between height and head circumference at the alphaequals0.01 level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals0 B. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 C. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 D. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0 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. Reject Upper H 0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance alphaequals0.01. B. Reject Upper H 0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance alphaequals0.01. C. Do not reject Upper H 0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance alphaequals0.01. D. Do not reject Upper H 0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance alphaequals0.01.

Answer 1

Regression Summary:

Regression Statistics
Multiple R	0.970494959
R Square	0.941860465
Adjusted R Square	0.92248062
Standard Error	0.074708737
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.271255814	0.271255814	48.6	0.006056849
Residual	3	0.016744186	0.005581395
Total	4	0.288
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	10.67674419	0.953519568	11.19719462	0.001526903	7.642219359	13.71126901	7.642219359	13.71126901
Height	0.251162791	0.036027752	6.971370023	0.006056849	0.136506404	0.365819177	0.136506404	0.365819177

A.

= 0.2512

s() = 0.036

B.

The correct answer is C. [Upper H 0​: beta1 = 0 ; Upper H 1​: beta1 equals0]

H₀: = 0

H₁: 0

p-value = 0.006

Conclusion:

Since p-value = 0.006 < 0.01 i.e. H₀ can be rejected.

The correct answer is: B

A. Reject Upper H 0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance of = 0.01.

Please upvote if you have liked my answer, would be of great help. Thank you.