A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are r = ±0.878, what can you conclude?

Null hypothesis:

Alternative hypothesis:

The statistic to check the hypothesis is given by:

And is distributed with n-2 degreed of freedom. df=n-2

For this case since the calculated values is on the interval (-0.878, 0.878) we can FAIL to reject the null hypothesis and on this case the correlation would be not significant at 5% of significance

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis:

Alternative hypothesis:

The statistic to check the hypothesis is given by:

And is distributed with n-2 degreed of freedom. df=n-2

For this case since the calculated values is on the interval (-0.878, 0.878) we can FAIL to reject the null hypothesis and on this case the correlation would be not significant at 5% of significance

option (a)

step-by-step explanation:

step 1:   take 2 number whose product equal to 25..

and sum of those two number are -10

step: 2 for example here if we take 5,5 are the number,,

5*5=25

and

5+5=10

but we need -10

so if we take   -5,-5

so -5*-5=25

and -5+(-5)=-10

s0

come the equation

replace -10x by these number

like -5x -5x+25

take common

x(x-5)-5(x-5)=0

(x-5)(x-5)=0