(a) Treating height as the explanatory variable, x, use technology to determine the estimates of
beta 0β0
and
beta 1β1.
beta 0β0almost equals≈b 0b0equals=
(Round to four decimal places as needed.)
beta 1β1almost equals≈b 1b1equals=
(Round to four decimal places as needed.)
(b) Use technology to compute the standard error of the estimate,
s Subscript ese.
s Subscript eseequals=
(Round to four decimal places as needed.)
(c) A normal probability plot suggests that the residuals are normally 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 are normally distributed. Test whether a linear relation exists between height and head circumference at the
alphaαequals=
level of significance. State the null and alternative hypotheses for this test.
Choose the correct answer below.
Upper H 0H0:
beta 0β0equals=0
Upper H 1H1:
beta 0β0not equals≠0
Upper H 0H0:
beta 0β0equals=0
Upper H 1H1:
beta 0β0greater than>0
Upper H 0H0:
beta 1β1equals=0
Upper H 1H1:
beta 1β1not equals≠0
Your answer is correct.
Upper H 0H0:
beta 1β1equals=0
Upper H 1H1:
beta 1β1greater than>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?
RejectReject
Upper H 0H0
and conclude that a linear relation
existsexists
between a child's height and head circumference at the level of significance
alphaαequals=
Your answer is correct.
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 of significance
alphaαequals=
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 of significance
alphaαequals=
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 of significance
alphaαequals=
(e) Use technology to
construct
a 95% confidence interval about the slope of the true least-squares regression line.
Lower bound:
Upper bound:
(Round to three decimal places as needed.)
(f) Suppose a child has a height of 26.5 inches. What would be a good guess for the child's head circumference?
A good estimate of the child's head circumference would be
inches.
(Round to two decimal places as needed.)