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, treating height as the explanatory variable and weight as the response variable.

​

(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=4.058x−93.9

B.

ŷ =8.058x−93.9

C.

ŷ =4.058x−95.9

D.

ŷ =−93.9x+4.058

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

B.

Reject H0. There is 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.

Do not 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.

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?

Yes

No

Answer 1

Applying regression on above data:

scatterplot is given above:

b)

A.

ŷ=4.058x−93.9

P-value for this hypothesis test =0.039

B: Reject H0. There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.

c) ​P-value= 0.076

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.

Yes