Question

the test statistic of ( z = 2.71 ) is obtained when testing the claim that ( p
eq0.784 ).
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.
b. p - value ( = 0.007 ) (round to three decimal places as needed.)
c. choose the correct conclusion below.
a. reject ( h_0 ). there is sufficient evidence to support the claim that ( p
eq0.784 ).
b. reject ( h_0 ). there is not sufficient evidence to support the claim that ( p
eq0.784 ).
c. fail to reject ( h_0 ). there is sufficient evidence to support the claim that ( p
eq0.784 ).
d. fail to reject ( h_0 ). there is not sufficient evidence to support the claim that ( p
eq0.784 ).

Explanation:

Step1: Determine the type of hypothesis test

The claim is \(p
eq0.784\). In hypothesis testing, when the alternative hypothesis is \(H_1: p
eq p_0\) (where \(p_0 = 0.784\) here), it is a two - tailed test.

Step2: Calculate the P - value

For a two - tailed \(z\) - test, the P - value is \(2\times(1 - P(Z<|z|))\). Given \(z = 2.71\). From the standard normal distribution table, \(P(Z < 2.71)=0.9966\). Then \(P - value=2\times(1 - 0.9966)=2\times0.0034 = 0.0068\approx0.007\)

Step3: Make a decision

The significance level \(\alpha = 0.05\). Since the P - value (\(0.007\)) is less than \(\alpha\) (\(0.05\)), we reject \(H_0\). When we reject \(H_0\), we have sufficient evidence to support the claim \(p
eq0.784\)

Answer:

a. Two - tailed test
b. \(0.007\)
c. A. Reject \(H_0\). There is sufficient evidence to support the claim that \(p
eq0.784\)