Question

Find the appropriate rejection regions for the large-sample test statistic z in these cases. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)(a) A right-tailed test with α=0.01z >z <(b) A two-tailed test at the 5% significance levelz > _z < _

Answer 1

a) We have that the significance is given by
`\alpha =0.01` and we know that we have a right tailed test.

So for this case we need to look in the normal standard dsitribution a critical value that accumulates 1% of the area on the right and 99% of the area on the left. This value can be founded with the following excel code:

"=NORM.INV(1-0.01,0,1)"

And we got for this case
`z_(crit)=2.33`

So then the rejection region would be
`z>2.33`

b) We have that the significance is given by
`\alpha =0.05`,
`\alpha/2 =0.025` and we know that we have a two tailed test.

So for this case we need to look in the normal standard dsitribution a critical value that accumulates 2.5% of the area on the right and 97.5% of the area on the left. This value can be founded with the following excel code:

"=NORM.INV(1-0.025,0,1)"

And we got for this case
`z_(crit)=\pm 1.96`

So then the rejection region would be
`z>1.96 \cup z<-1.96`

Explanation:

Part a

We have that the significance is given by
`\alpha =0.01` and we know that we have a right tailed test.

So for this case we need to look in the normal standard dsitribution a critical value that accumulates 1% of the area on the right and 99% of the area on the left. This value can be founded with the following excel code:

"=NORM.INV(1-0.01,0,1)"

And we got for this case
`z_(crit)=2.33`

So then the rejection region would be
`z>2.33`

Part b

We have that the significance is given by
`\alpha =0.05`,
`\alpha/2 =0.025` and we know that we have a two tailed test.

So for this case we need to look in the normal standard dsitribution a critical value that accumulates 2.5% of the area on the right and 97.5% of the area on the left. This value can be founded with the following excel code:

"=NORM.INV(1-0.025,0,1)"

And we got for this case
`z_(crit)=\pm 1.96`

So then the rejection region would be
`z>1.96 \cup z<-1.96`