Zachary completes a hypothesis test and finds that he rejects the null hypothesis. which statement gives a reason for rejecting
the null hypothesis?
the z-statistic is less than 0.
the z-statistic lies in the critical region.
the z-statistic lies outside the critical region.
the z-statistic is greater than 0.

The z-statistic lies in the critical region

Step-by-step explanation:

When a hypothesis test is performed, the decision to reject or not reject the null hypothesis is made on basis of following observations:

In the given statement Zachary rejects the Null Hypothesis, this means the z-statistic she calculated must have been inside the critical or rejection region. Hence the correct answer would be:

The z-statistic lies in the critical region

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

$12. that is my answer.