Question

Find the​ P-value for the indicated hypothesis test with the given standardized test​ statistic, z. Decide whether to reject

Upper H 0H0

for the given level of significance

alphaα.

​Two-tailed test with test statistic

z=- −2.15 0.08

test statistic

z= -2.15 and α=0.08

​P-value=_____

​(Round to four decimal places as​ needed.)

2)Find the critical​ value(s) and rejection​ region(s) for the indicated​ t-test, level of significance

α​,and sample size n. Left​-tailed ​test,

α=0.10​,

n=13

The critical​ value(s) is/are

Answer 1

1 )

Given that test is two tailed test.

test statistics = z = -2.15 , = 0.08

P- value for this two tailed test is given by,

P-value = 2* P( z < -2.15 )

Using Excel function,   =NORMSDIST( z )

P( z < -2.15 ) = NORMSDIST( -2.15 ) = 0.015778

So, P-value = 2* 0.015778 = 0.0316

Decision rule - If P-value > then fail to reject null hypothesis.                          If p-value <= then reject null hypothesis.

Here it is observed that p-value = 0.0316 is less than = 0.08.

So , Reject null hypothesis ( H₀ )

2)

Given t- test is left tailed test.

n = 13 , = 0.10

degrees of freedom = df = n - 1 = 13 - 1 = 12

The critical​ value for this left tailed test is,

Using Excel function,    =T.INV( Probability, df )

=T.INV( 0.1 , 12 ) = -1.3562

The critical​ value is -1.3562

If test statistics less than -1.3562 then reject null hypothesis.

Rejection region = R ={t : t < -1.3562 }