When testing whether the correlation coefficient differs from zero, the value of the test statistic is t20 = −2.95 with a corresponding p-value of 0.0061. At the 5% significance level, can you conclude that the correlation coefficient differs from zero?
A) Yes, since the p-value is less than 0.05.
B) Yes, since the absolute value of the test statistic exceeds 0.05.
C) No, since the p-value is less than 0.05.
D) No, since the absolute value of the test statistic exceeds 0.05.

A. Yes, since the p-value is less than 0.05.

Step-by-step explanation:

For the testing of correlation coefficient the null hypothesis and alternative hypothesis can be stated as

Null hypothesis: The correlation coefficient doesn't differs from zero.

Alternative hypothesis: The correlation coefficient differs from zero.  

If our p-value is less than significance level α then the null hypothesis will be rejected. We are given that p-value=0.0061 and α=0.05.

As we can see that p-value is much smaller than α, so, the null hypothesis will be rejected and we conclude that the correlation coefficient differs from zero.

So, the correct option is option A which is "Yes, since the p-value is less than 0.05".

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

i think it is 70

step-by-step explanation: