Find the P-value for the indicated hypothesis test with the given standardized test statistic, $z$. Decide whether to reject $\mathrm{H}_{0}$ for the given level of significance $\alpha$.
Right-tailed test with test statistic $z=1.93$ and $\alpha=0.06$
$\mathrm{P}$-value $=\square$ (Round to four decimal places as needed. $)$

Step 1 ：We are given a right-tailed test with test statistic \(z=1.93\) and level of significance \(\alpha=0.06\).

Step 2 ：The P-value is the probability that a random variable under the null hypothesis exceeds the observed test statistic. In a right-tailed test, this is the area to the right of the test statistic on the standard normal distribution.

Step 3 ：To find the P-value, we need to find the area to the right of \(z=1.93\) on the standard normal distribution. This can be done using the cumulative distribution function (CDF) of the standard normal distribution, which gives the probability that a standard normal random variable is less than or equal to a given value. The area to the right of a given value is then \(1 - \text{CDF}(z)\).

Step 4 ：After calculating, we find that the P-value is approximately 0.0268.

Step 5 ：We then compare the P-value with the level of significance \(\alpha=0.06\) to decide whether to reject the null hypothesis \(\mathrm{H}_{0}\). If the P-value is less than \(\alpha\), we reject \(\mathrm{H}_{0}\). Otherwise, we do not reject \(\mathrm{H}_{0}\).

Step 6 ：Since the P-value is less than the level of significance, we reject the null hypothesis \(\mathrm{H}_{0}\).

Step 7 ：Final Answer: \(\boxed{0.0268}\)