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 25 27.5 27 25.5 26 Head Circumference​ (inches), y 16.9 17.5 17.5 17.1 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 1equals0 Upper H 1​: beta 1greater than0 C. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 D. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 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 exists between a​ child's height and head circumference at the level of significance alphaequals0.01. B. 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. 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. 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. Click to select your answer(s).

Answer 1

Regression Summary from excel:

Regression Statistics
Multiple R	0.961644738
R Square	0.924760602
Adjusted R Square	0.899680803
Standard Error	0.082593616
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.251534884	0.251534884	36.87272727	0.008965134
Residual	3	0.020465116	0.006821705
Total	4	0.272
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	10.92325581	1.044204174	10.46084289	0.001864939	7.600132097	14.24637953	4.82415393	17.0223577
Height	0.241860465	0.039830179	6.072291764	0.008965134	0.115103061	0.36861787	0.009216004	0.474504926

A.

= 0.2419

s() = 0.0398

B.

The correct answer is D.

H₀: = 0

H₁: 0

p-value = 0.00897

Conclusion:

Since p-value = 0.00897 < 0.01 i.e. H₀ can be rejected.

The correct answer is: A

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

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