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 α=0.01. President (cm)    Opponent (cm) 173    178 187    176 190    179 180    171 175    180 183    181 191    176 180    178 177    178 190    176 190    178 185    192 181    179 190    172 Determine the null and alternative hypotheses.   enter your response here ​(Type integers or decimals. Do not​ round.) Part 4 The test statistic is t=enter your response here. ​(Round to two decimal places as​ needed.) Part 5 The​ P-value is enter your response here. ​(Round to three decimal places as​ needed.) Part 6 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. Part 7 Should we expect that there would be a​ correlation?     A. ​No, because presidential candidates are nominated for reasons other than height.   B. ​Yes, because presidential candidates are nominated for reasons other than height.   C. ​No, because height is the main reason presidential candidates are nominated.   D. ​Yes, because height is the main reason presidential candidates are nominated.

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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 α=0.01.

President (cm)    Opponent (cm)
173    178
187    176
190    179
180    171
175    180
183    181
191    176
180    178
177    178
190    176
190    178
185    192
181    179
190    172

Determine the null and alternative hypotheses.
 
enter your response here
​(Type integers or decimals. Do not​ round.)
Part 4
The test statistic is
t=enter your response here.
​(Round to two decimal places as​ needed.)
Part 5
The​ P-value is
enter your response here.
​(Round to three decimal places as​ needed.)
Part 6
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.
Part 7
Should we expect that there would be a​ correlation?
 
 
A.
​No, because presidential candidates are nominated for reasons other than height.
 
B.
​Yes, because presidential candidates are nominated for reasons other than height.
 
C.
​No, because height is the main reason presidential candidates are nominated.
 
D.
​Yes, because height is the main reason presidential candidates are nominated.
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