Question

The data in the accompanying table represent the heights and weights of a random sample of professional baseball players. Complete parts ​(a) through ​(c) below.

Player   Height_(inches)   Weight_(pounds)
Player_1   75   227
Player_2   75   195
Player_3   72   180
Player_4   82   231
Player_5   69   185
Player_6   74   190
Player_7   75   228
Player_8   71   200
Player_9   75   230

​(a) Draw a scatter diagram of the​ data

​(b) Determine the​ least-squares regression line. Test whether there is a linear relation between height and weight at the α=0.05 level of significance.

Determine the​ least-squares regression line. Choose the correct answer below.

A.

ŷ =−93.9x+4.058

B.

ŷ =4.058x−93.9

C.

ŷ =4.058x−95.9

D.

ŷ =8.058x−93.9

Test whether there is a linear relation between height and weight at the α=0.05 level of significance.

State the null and alternative hypotheses. Choose the correct answer below.

A.

H0​: β1=0

H1​: β1>0

B.

H0​: β0=0

H1​: β0≠0

C.

H0​: β1=0

H1​: β1≠0

D.

H0​: β0=0

H1​: β0>0

Determine the​ P-value for this hypothesis test.

​P-value=__?__

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

State the appropriate conclusion at the α=0.05 level of significance. Choose the correct answer below.

A.

Reject H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

B.

Reject H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

C.

Do not reject H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

D.

Do not reject H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

​(c) Remove the values listed for Player 4 from the data table. Test whether there is a linear relation between height and weight. Do you think that Player 4 is​ influential?

Determine the​ P-value for this hypothesis test.

​P-value=__?__

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

State the appropriate conclusion at the α=0.05 level of significance. Choose the correct answer below.

A.

Reject H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

B.

Do not reject H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

C.

Do not reject H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

D.

Reject H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

Do you think that Player 4 is​ influential?

No

Yes

Answer 1

	H(x)	W(y)
P1	75	227
P2	75	195
P3	72	180
P4	82	231
P5	69	185
P6	74	190
P7	75	228
P8	71	200
P9	75	230

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.691020025
R Square	0.477508676
Adjusted R Square	0.402867058
Standard Error	16.48318806
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1738.131579	1738.131579	6.397351635	0.039273172
Residual	7	1901.868421	271.6954887
Total	8	3640
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-93.85263158	119.205537	-0.78731772	0.456920945	-375.7289353	188.0236721	-375.7289353	188.0236721
H(x)	4.057894737	1.604355715	2.529298645	0.039273172	0.264196305	7.851593169	0.264196305	7.851593169

ŷ =4.058 * x − 93.9

W = 4.058 * H − 93.9

H0​: β0=0

H1​: β0≠0

P value = 0.039(from above table) < 0.05

Reject H0.

There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

	H(x)	W(y)
P1	75	227
P2	75	195
P3	72	180
P5	69	185
P6	74	190
P7	75	228
P8	71	200
P9	75	230

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.658557069
R Square	0.433697413
Adjusted R Square	0.339313648
Standard Error	16.85477183
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1305.375	1305.375	4.595042534	0.075772266
Residual	6	1704.5	284.0833333
Total	7	3009.875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-227.8	201.6993486	-1.129403747	0.30184836	-721.3405255	265.7405255	-721.3405255	265.7405255
H(x)	5.9	2.752372714	2.143605032	0.075772266	-0.834813399	12.6348134	-0.834813399	12.6348134

P value = 0.07577 > 0.05

Do not reject H0.

There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

YES Player 4 is​ influential