Question

the test statistic of ( z = 1.33 ) is obtained when testing the claim that ( p
eq 0.675 ).
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 = 0.10 ), 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

Explanation:

Step1: Determine the type of test

The claim is \(p
eq0.675\). In hypothesis testing, when the alternative hypothesis is \(H_1: p
eq p_0\) (where \(p_0 = 0.675\) here), it is a two - tailed test.

Step2: Calculate the P - value

For a two - tailed test with \(z = 1.33\), the P - value is \(2\times(1 - P(Z<1.33))\).
From the standard normal distribution table, \(P(Z < 1.33)=0.9082\).
So, \(P - value=2\times(1 - 0.9082)=2\times0.0918 = 0.1836\).

Step3: Make a decision

We are given \(\alpha=0.10\).
Since the P - value (\(0.1836\)) > \(\alpha(0.10)\), we fail to reject \(H_0\).

Answer:

a. Two - tailed
b. \(0.1836\)
c. Fail to reject \(H_0\)