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   76   227
Player_2   75   197
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

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

alphaαequals=0.05

level of significance.

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

A.

ModifyingAbove y with caretyequals=4.1604.160xnegative 103.7−103.7

B.

ModifyingAbove y with caretyequals=8.160xnegative−101.7

C.

ModifyingAbove y with caretyequals=negative 101.7−101.7xplus+4.1604.160

D.

ModifyingAbove y with caretyequals=4.1604.160xnegative 101.7−101.7

Test whether there is a linear relation between height and weight at the

alphaαequals=0.05

level of significance.

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

A.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1not equals≠0

B.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0not equals≠0

C.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0greater than>0

D.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1greater than>0

Determine the​ P-value for this hypothesis test.

​P-valueequals=nothing

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

State the appropriate conclusion at the

alphaαequals=0.05

level of significance. Choose the correct answer below.

A.Do not reject

Upper H 0H0.

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

B.Do not reject

Upper H 0H0.

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

C.Reject

Upper H 0H0.

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

D.Reject

Upper H 0H0.

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-valueequals=nothing

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

State the appropriate conclusion at the

alphaαequals=0.05

level of significance. Choose the correct answer below.

A.Reject

Upper H 0H0.

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

B.Do not reject

Upper H 0H0.

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

C.Do not reject

Upper H 0H0.

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

D.Reject

Upper H 0H0.

There is 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?

Yes

No

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	669.00	1868.00	108.00	3594.22	449.33
mean	74.33	207.56	SSxx	SSyy	SSxy

.

sample size ,   n =   9      
here, x̅ = Σx / n=   74.333          
ȳ = Σy/n =   207.556          
SSxx =    Σ(x-x̅)² =    108.0000      
SSxy=   Σ(x-x̅)(y-ȳ) =   449.3      
              
estimated slope , ß1 = SSxy/SSxx =   449.3333/108=   4.16049      
intercept,ß0 = y̅-ß1* x̄ =   207.5556- (4.1605 )*74.3333=   -101.70782      

b)

D. Y^=4.160*X −101.7

c)

Ho:   β1=   0
H1:   β1╪   0

estimated std error of slope =Se(ß1) = Se/√Sxx =    15.697/√108=   1.5104
t stat = estimated slope/std error =ß1 /Se(ß1) =    (4.1605-0)/1.5104=   2.7545
Degree of freedom ,df = n-2=   7  
t-critical value=    2.3646   [excel function: =T.INV.2T(α,df) ]
      
p-value =    0.028

D.Reject

Upper H 0H0.

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

c)

p value=0.053

B.Do not reject Ho.

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

YES, influential