height and head circumference. The data are summarized below.Complete parts? (a) through? (f) below.
Height? (inches), x | 2727 | 27.527.5 | 26.526.5 | 2626 | 24.524.5 | |
|---|
Head Circumference? (inches), y | 17.517.5 | 17.517.5 | 17.317.3 | 17.317.3 | 17.117.1 | |
|---|
?(a) Treating height as the explanatory? variable, x, usetechnology to determine the estimates of
beta 0?0
and
beta 1?1.
beta 0?0almost equals?b 0b0equals=
nothing ?(Round to four decimal places as? needed.)beta1?1almost equals?b 1b1equals=
nothing ?(Round to four decimal places as? needed.)
B Use technology to compute the standard errorof the? estimate,
s Subscript ese.
s Subscript eseequals=
?(Round to four decimal places as? needed.)
?(c) A normal probability plot suggests that the residuals arenormally distributed. Use technology to determine
s Subscript b 1sb1.
s Subscript b 1sb1equals=??
?(Round to four decimal places as? needed.)
?(d) A normal probability plot suggests that the residuals arenormally distributed. Test whether a linear relation exists betweenheight and head circumference at the
alpha?equals=0.010.01
level of significance. State the null and alternative hypothesesfor this test.
Choose the correct answer below.
A.
Upper H 0H0?:
beta 1?1equals=0
Upper H 1H1?:
beta 1?1not equals?0
Your answer is correct.
B.
Upper H 0H0?:
beta 1?1equals=0
Upper H 1H1?:
beta 1?1greater than>0
C.
Upper H 0H0?:
beta 0?0equals=0
Upper H 1H1?:
beta 0?0greater than>0
D.
Upper H 0H0?:
beta 0?0equals=0
Upper H 1H1?:
beta 0?0not equals?0
Determine the? P-value for this hypothesis test.
?P-valueequals=
?(Round to three decimal places as? needed.)
What is the conclusion that can be? drawn?
A.
RejectReject
Upper H 0H0
and conclude that a linear relation
existsexists
between a? child's height and head circumference at the level ofsignificance
alpha?equals=0.010.01.
Your answer is correct.
B.
Do not rejectDo not reject
Upper H 0H0
and conclude that a linear relation
does not existdoes not exist
between a? child's height and head circumference at the level ofsignificance
alpha?equals=0.010.01.
C.
RejectReject
Upper H 0H0
and conclude that a linear relation
does not existdoes not exist
between a? child's height and head circumference at the level ofsignificance
alpha?equals=0.010.01.
D.
Do not rejectDo not reject
Upper H 0H0
and conclude that a linear relation
existsexists
between a? child's height and head circumference at the level ofsignificance
alpha?equals=0.010.01.
?(e) Use technology to
construct
a? 95% confidence interval about the slope of the true?least-squares regression line.
Lower? bound:
Upper? bound: 0.351
?(Round to three places as? needed.)
?(f) Suppose a child has a height of 26.5 inches. What would bea good guess for the? child's head? circumference?
A good stimate of the? child's head circumference would beinches.
?(Round to two decimal places as? needed.)
