Question

Media periodically discuss the issue of heights of winning presidential candidates and heights of their main opponents. The accompanying table lists the heights​ (cm) from several recent presidential elections. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a​ correlation? Use a significance level of alphaαequals=0.05.

President (cm)   Opponent (cm)
174   180
187   184
193   184
177   175
176   180
178   185
194   181
180   185
176   179
184   175
191   177
183   194
187   189
185   170

Construct a scatterplot. Choose the correct graph below.

A.

160200160200President Height (cm)Opponent Height (cm)

A scatterplot has a horizontal axis labeled President Height in centimeters from 160 to 200 in increments of 5 and a vertical axis labeled Opponent Height in centimeters from 160 to 200 in increments of 5. Fourteen points are plotted with approximate coordinates as follows: (174, 180); (187, 176); (193, 176); (177, 185); (176, 180); (178, 175); (194, 179); (180, 175); (176, 181); (184, 185); (191, 183); (183, 166); (187, 171); (185, 190).

B.

160200160200President Height (cm)Opponent Height (cm)

A scatterplot has a horizontal axis labeled President Height in centimeters from 160 to 200 in increments of 5 and a vertical axis labeled Opponent Height in centimeters from 160 to 200 in increments of 5. Fourteen points are plotted with approximate coordinates as follows: (174, 180); (187, 184); (193, 184); (177, 175); (176, 180); (178, 185); (194, 181); (180, 185); (176, 179); (184, 175); (191, 177); (183, 194); (187, 189); (185, 170).

C.

160200160200President Height (cm)Opponent Height (cm)

A scatterplot has a horizontal axis labeled President Height in centimeters from 160 to 200 in increments of 5 and a vertical axis labeled Opponent Height in centimeters from 160 to 200 in increments of 5. Fourteen points are plotted with approximate coordinates as follows: (186, 180); (173, 176); (167, 176); (183, 185); (184, 180); (182, 175); (166, 179); (180, 175); (184, 181); (176, 185); (169, 183); (177, 166); (173, 171); (175, 190).

D.

160200160200President Height (cm)Opponent Height (cm)

A scatterplot has a horizontal axis labeled President Height in centimeters from 160 to 200 in increments of 5 and a vertical axis labeled Opponent Height in centimeters from 160 to 200 in increments of 5. Fourteen points are plotted with approximate coordinates as follows: (186, 180); (173, 184); (167, 184); (183, 175); (184, 180); (182, 185); (166, 181); (180, 185); (184, 179); (176, 175); (169, 177); (177, 194); (173, 189); (175, 170).The linear correlation coefficient r is

nothing.

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

Determine the null and alternative hypotheses.

Upper H 0H0​:

rhoρ

▼

less than<

greater than>

equals=

not equals≠

nothing

Upper H 1H1​:

rhoρ

▼

greater than>

equals=

not equals≠

less than<

nothing

​(Type integers or decimals. Do not​ round.)

The test statistic is

nothing.

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

The​ P-value is

nothing.

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

Because the​ P-value of the linear correlation coefficient is

▼

greater than

less than or equal to

the significance​ level, there

▼

is not

is

sufficient evidence to support the claim that there is a linear correlation between the heights of winning presidential candiates and the heights of their opponents.

Should we expect that there would be a​ correlation?

A.

​No, because height is the main reason presidential candidates are nominated.

B.

​Yes, because presidential candidates are nominated for reasons other than height.

C.

​No, because presidential candidates are nominated for reasons other than height.

D.

​Yes, because height is the main reason presidential candidates are nominated.

Click to select your answer(s).

Answer 1

Let the height of presidential election candidate: be X

and that of the opponent be Y

Scatter Plot

Option B is right

Q) is there sufficient evidence to support the claim that there is a linear correlation between the heights of winning presidential candidates and the heights of their opponents.

A) ​No, because presidential candidates are nominated for reasons other than height.