Question

the test statistic of ( z = 1.40 ) is obtained when testing the claim that ( p>0.5 ).
a. identify the hypothesis test as being two - tailed, left - tailed, or right - tailed.
b. find the p - value.
c. using a significance level of ( alpha = 0.01 ), should we reject ( h_0 ) or should we fail to reject ( h_0 )?
click here to view page 1 of the standard normal distribution table.
click here to view page 2 of the standard normal distribution table.
a. this is a test.

Explanation:

Step1: Determine the type of test

The claim is \(p > 0.5\). In hypothesis testing, if the alternative hypothesis is of the form \(H_1:p>p_0\) (where \(p_0 = 0.5\) here), the test is right - tailed.

Step2: Calculate the P - value

For a right - tailed z - test, the P - value is \(P(Z>z)\). Given \(z = 1.40\).
We know that \(P(Z>1.40)=1 - P(Z\leq1.40)\).
From the standard normal distribution table, \(P(Z\leq1.40)=0.9192\).
So \(P(Z > 1.40)=1-0.9192 = 0.0808\).

Step3: Make a decision

The significance level \(\alpha=0.01\).
We compare the P - value with \(\alpha\). If \(P - value<\alpha\), we reject \(H_0\); if \(P - value\geq\alpha\), we fail to reject \(H_0\).
Since \(P - value=0.0808\) and \(\alpha = 0.01\), and \(0.0808>0.01\).

Answer:

a. This is a right - tailed test.
b. The P - value is \(0.0808\).
c. We fail to reject \(H_0\).