Question

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

Upper H0

for the given level of significance

alphaα.

​Two-tailed test with test statistic

zequals=−2.18

and

alphaαequals=0.04

​P-valueequals=

p-value=___ (round to four decimal places if needed)

state your conclusion.

fail to reject or reject h0

#38

Answer 1

Solution:

We have to find the​ P-value for the indicated hypothesis test with the given standardized test​ statistic, z

Two-tailed test with test statistic and z = - 2.18

Level of significance =

Since this is two tailed test, P-value is given by:

P-value = 2 X P( Z < z test statistic value)

( Note we use Z < z when z value is negative and Z > z when z is positive)

P-value = 2 X P( Z < -2.18)

Look in z table for z = -2.1 and 0.08 and find corresponding area.

P( Z < -2.18) = 0.0146

Thus P-value is:

P-value = 2 X P( Z < -2.18)

P-value = 2 X 0.0146

P-value = 0.0292

State your conclusion:

Since P-value = 0.0292 < 0.04 significance level, we reject null hypothesis H0.

Reject H0.