The maximum weights​ (in kilograms) for which one repetition of a​ half-squat can be performed and the jump heights​ (in centimeters) for 12 international soccer players are given in the accompanying table. The correlation​ coefficient, rounded to three decimal​ places, is r=0.766. At α=0.05​, is there enough evidence to conclude that there is a significant linear correlation between the​ variables? Soccer player data Maximum_weight,_x   Jump_height,_y 190                                   60 185                                   57 155                                   54 180                                   61 175                                   57 170                                   65 150                                   51 160                                   52 160                                   50 180                                   57 190                                   60 210                                   65 Determine the null and alternative hypotheses. choose the best answer H0​:ρ▼ a.greater than or equals≥ b.less than or equals≤ c.less than< d.equals= e.not equals≠ g.greater than> 0 Ha​:ρ▼ A.less than< b.equals= c.less than or equals≤ d.greater than or equals≥ e.greater than> f.not equals≠     Determine the critical​ value(s).   t0= ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)   Determine the standardized test statistic.   t= ​(Round to three decimal places as​ needed.)   What is the​ conclusion? choose a or b ▼   a.Reject b.Fail to reject H0. There ▼   a.is not b.is enough evidence at the 5​% level of significance to conclude that there is a significant linear correlation between the maximum weight for one repetition of a half squat and the jump height.

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The maximum weights​ (in kilograms) for which one repetition of a​ half-squat can be performed and the jump heights​ (in centimeters) for

12

international soccer players are given in the accompanying table. The correlation​ coefficient, rounded to three decimal​ places, is

r=0.766.

At

α=0.05​,

is there enough evidence to conclude that there is a significant linear correlation between the​ variables?

Soccer player data

Maximum_weight,_x   Jump_height,_y
190                                   60
185                                   57
155                                   54
180                                   61
175                                   57
170                                   65
150                                   51
160                                   52
160                                   50
180                                   57
190                                   60
210                                   65

Determine the null and alternative hypotheses.
choose the best answer
H0​:ρ
a.greater than or equals≥
b.less than or equals≤
c.less than<
d.equals=
e.not equals≠
g.greater than>
0
Ha​:ρ
A.less than<
b.equals=
c.less than or equals≤
d.greater than or equals≥
e.greater than>
f.not equals≠

 

 

Determine the critical​ value(s).
 
t0=
​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)
 
Determine the standardized test statistic.
 
t=
​(Round to three decimal places as​ needed.)
 
What is the​ conclusion?
choose a or b
 
a.Reject
b.Fail to reject
H0.
There
 
a.is not
b.is
enough evidence at the
5​%
level of significance to conclude that there is a significant linear correlation between the maximum weight for one repetition of a half squat and the jump height.
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