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)
176   179
184   181
191   186
176   174
184   181
179   183
190   183
180   182
179   187
183   172
187   174
191   182
182   186
183   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: (184, 179); (176, 181); (169, 186); (184, 174); (176, 181); (181, 183); (170, 183); (180, 182); (181, 187); (177, 172); (173, 174); (169, 182); (178, 186); (177, 170).

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: (184, 181); (176, 179); (169, 174); (184, 186); (176, 179); (181, 177); (170, 177); (180, 178); (181, 173); (177, 188); (173, 186); (169, 178); (178, 174); (177, 190).

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: (176, 181); (184, 179); (191, 174); (176, 186); (184, 179); (179, 177); (190, 177); (180, 178); (179, 173); (183, 188); (187, 186); (191, 178); (182, 174); (183, 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: (176, 179); (184, 181); (191, 186); (176, 174); (184, 181); (179, 183); (190, 183); (180, 182); (179, 187); (183, 172); (187, 174); (191, 182); (182, 186); (183, 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

▼

equals=

not equals≠

less than<

greater than>

nothing

Upper H 1H1​:

rhoρ

▼

greater than>

less than<

equals=

not equals≠

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

▼

less than or equal to

greater than

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.

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

D.

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

Click to select your answer(s).

Answer 1

Solution:-) I have used R to solve the problems, On uper side is output and on lower side is R Code.

So, scatter plot is given above

B) Now we have to test for correlation , So the hypotheses is stated as

Null hypothesis is height iand presidential candidates are correlated and alternative hypotheses is that height iand presidential candidates are not related and hence they did not have effect on each other.

We get the following output

t = 0.58679, df = 12, p-value = 0.5682

As p-value > 0.05(significance level), hence we fail to reject the null hypothesis. Therefore,

​there is no correlation and  because presidential candidates are nominated for reasons other than height.