Question

find the p - value for a left - tailed hypothesis test with a test statistic of ( z=-1.08 ). decide whether to reject ( h_{0} ) if the level of significance is ( alpha = 0.05 ).

p - value ( =square ) (round to four decimal places as needed.)

Explanation:

Step1: Recall the formula for P - value in left - tailed test

For a left - tailed \(z\) - test, the \(P\) - value is \(P(Z\lt z)\), where \(Z\) is a standard normal random variable and \(z=- 1.08\).

Step2: Use the standard normal table or a calculator

Using a standard normal table (or a calculator with a normal distribution function, e.g., in Excel: NORM.S.DIST(-1.08,TRUE)), we find that \(P(Z\lt - 1.08)\).
From the standard normal table, \(P(Z\lt - 1.08)=0.1401\)

Step3: Compare the P - value with the significance level

We have \(\alpha = 0.05\) and \(P - value=0.1401\). Since \(P - value(0.1401)\gt\alpha(0.05)\), we do not reject \(H_0\)

Answer:

\(P - value = 0.1401\), do not reject \(H_0\)