Question

the test statistic of ( z = 2.20 ) is obtained when testing the claim that ( p
eq0.855 ).
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 \(p
eq0.855\). In hypothesis testing, when the alternative hypothesis is of the form \(H_1:p
eq p_0\) (where \(p_0 = 0.855\) in this case), the test is two - tailed.

Step2: Calculate the P - value

For a two - tailed \(z\) - test, the P - value is \(2\times(1 - P(Z<|z|))\). Given \(z = 2.20\).
From the standard normal distribution table, \(P(Z < 2.20)=0.9861\).
So the P - value \(=2\times(1 - 0.9861)=2\times0.0139 = 0.0278\).

Step3: Make a decision

We are given \(\alpha=0.01\).
Since the P - value (\(0.0278\))> \(\alpha(0.01)\), we fail to reject \(H_0\).

Answer:

a. This is a two - tailed test.
b. The P - value is \(0.0278\).
c. We should fail to reject \(H_0\).