Question

the test statistic in a two - tailed test is ( z = 2.74 ). determine the p - value for a two - tailed z test.
the p - value is (square).
(round to four decimal places as needed.)

Explanation:

Step1: Find the probability for one - tail

For a standard normal distribution \(Z\), we first find \(P(Z>2.74)\). Using the standard normal table or a calculator with a normal - distribution function (e.g., in Excel: =1 - NORM.S.DIST(2.74,TRUE) or in R: 1 - pnorm(2.74)).
\(P(Z > 2.74)=1 - P(Z\leq2.74)\)
From the standard normal table, \(P(Z\leq2.74)=0.9969\)
So \(P(Z > 2.74)=1 - 0.9969 = 0.0031\)

Step2: Calculate the two - tailed P - value

For a two - tailed \(z\) - test, the \(P\) - value is \(P = 2\times P(Z>z)\) (when \(z>0\)).
Since \(z = 2.74>0\), then \(P=2\times0.0031\)

Answer:

\(0.0062\)