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.
a. this is a two - tailed test.
b. ( p - value=) (round to three decimal places as needed.)

Explanation:

Step1: Find the area corresponding to \(z = 2.71\)

For a standard normal distribution \(Z\sim N(0,1)\), we look up the value of \(P(Z < 2.71)\) in the standard - normal table. From the standard normal table, \(P(Z < 2.71)=0.9966\).

Step2: Calculate the one - tailed \(P\) - value

The one - tailed \(P\) - value is \(P(Z>2.71)=1 - P(Z < 2.71)\). So \(P(Z>2.71)=1 - 0.9966 = 0.0034\).

Step3: Calculate the two - tailed \(P\) - value

Since this is a two - tailed test (\(p
eq p_0\)), the \(P\) - value is \(P = 2\times P(Z>2.71)\). Substituting the value from Step 2, we get \(P=2\times0.0034 = 0.0068\approx0.007\)

Answer:

\(0.007\)