Question

the test statistic of ( z = 1.42 ) is obtained when testing the claim that ( p>0.2 ).
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 = 0.05 ), 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
right - tailed
left - tailed
two - tailed

Explanation:

Step1: Identify the type of test

Since the claim is \(p > 0.2\), we are looking at the right - hand tail of the distribution. So this is a right - tailed test.

Step2: Find the P - value

For a right - tailed \(z\) - test with \(z = 1.42\), we look up the value of \(P(Z\leq1.42)\) in the standard normal table. From the standard normal table, \(P(Z\leq1.42)=0.9222\). Then the \(P\) - value is \(P = 1 - P(Z\leq1.42)\).

$$P=1 - 0.9222=0.0778$$

Step3: Make a decision

We are given \(\alpha = 0.05\). Since \(P - value=0.0778>0.05=\alpha\), we fail to reject \(H_0\) (the null hypothesis).

Answer:

a. right - tailed
b. \(0.0778\)
c. fail to reject \(H_0\)