Question

find the p - value for the indicated hypothesis test with the given standardized test statistic, z. decide whether to reject ( h_0 ) for the given level of significance ( alpha ).
two - tailed test with test statistic ( z=-1.60 ) and ( alpha = 0.03 )
( p - value=square ) (round to four decimal places as needed.)

Explanation:

Step1: Find the area for one - tail

For a two - tailed test, first find the area corresponding to \(z=-1.60\). Using the standard normal distribution table (or a calculator with a normal - distribution function), the area to the left of \(z =-1.60\) is \(P(Z\lt - 1.60)\).
From the standard normal table, \(P(Z\lt -1.60)=0.0548\).

Step2: Calculate the P - value for two - tailed test

The formula for the P - value of a two - tailed test is \(P - value=2\times P(Z\lt|z|)\) (when \(z\lt0\)). Here \(|z| = 1.60\), so \(P - value=2\times0.0548\).
\(P - value = 0.1096\)

Step3: Make a decision

Compare the P - value with \(\alpha\). We have \(P - value=0.1096\) and \(\alpha = 0.03\). Since \(P - value(0.1096)\gt\alpha(0.03)\), we do not reject \(H_0\).

Answer:

The \(P\) - value is \(0.1096\). Do not reject \(H_0\) because \(P - value\gt\alpha\).