Pairs of P-values and significance levels, ?, are given. For each pair, state whether the observed P-value leads to rejection of H0 at the given significance level. Choose reject or fail to reject for each.

(a) P-value = .084, ? = .05

reject

fail to reject

(b) P-value = .003, ? = .001

reject

fail to reject

(c) P-value = .498, ? = .05

reject

fail to reject

(d) P-value = .084, ? = .10

reject

fail to reject

(e) P-value = .039, ? = .01

reject

fail to reject

(f) P-value = .056, ? = .10

reject

fail to reject

a)

fail to reject

b)

fail to reject

c)

fail to reject

d)

reject

e)

fail to reject

f)

reject

Step-by-step explanation:

We are given the p-values and significance level to decide whether the null hypothesis should be rejected or not. We reject the null hypothesis if the p-value is less than significance level and we fail to reject the null hypothesis if the p-value is greater than significance level.

a)

As p-value=0.084 is greater than significance level=0.05, so we fail to reject the null hypothesis.

b)

As p-value=0.003 is greater than significance level=0.001, so we fail to reject the null hypothesis.

c)

As p-value=0.498 is greater than significance level=0.05, so we fail to reject the null hypothesis.

d)

As p-value=0.084 is less than significance level=0.10, so we reject the null hypothesis.

e)

As p-value=0.039 is greater than significance level=0.01, so we fail to reject the null hypothesis.

f)

As p-value=0.056 is less than significance level=0.10, so we reject the null hypothesis.

(Exact Answer) When all the entries above the diagonal entries are 0, the solution will not be different from when all the entries below the diagonal entries are 0. This is because in both cases, there will be one row that would be left with just one unknown element, thus giving us the solution to the other unknowns through back-substitution. For instance, in a linear system with three unknowns, x, y, and z, the traditional triangulated form will give us the value of z first; however, if the entries above the diagonal entries in the matrix are 0, then we will get the value of x first. In either case, the solution will be the same.

Step-by-step explanation: