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 alphaequals0.01

PRESIDENT: 180 177 194 170 181 178 195 178 172 187 190 187 178 194

OPPONENT: 180 176 184 171 178 184 176 183 180 181 168 182 189 175

1. The linear correlation coefficient r is __________. ​(Round to three decimal places as​ needed.)

2. Determine the null and alternative hypotheses. (Type integers or decimals. Do not​ round.)

H 0​: p ______ _______

H1: p ______ _______

3. The​ P-value is ________. ​(Round to three decimal places as​ needed.)

4. Because the​ P-value of the linear correlation coefficient is ▼ less than or equal to, greater than the significance​ level, there ▼ is, is not 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.

5. Should we expect that there would be a​ correlation?

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

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

C. ​Yes, 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) and then click Check Answer.

Answer 1

1) The linear correlation coefficient r is -0.113

2)

null hypothesis:		ρ	=	0
Alternate Hypothesis:		ρ	≠	0

3)

The​ P-value is 0.701 (try 0.702 if this comes wrong)

4)

Because the​ P-value of the linear correlation coefficient is greater than the significance​ level, there is not 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

5)

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