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: \(\boxed{0.0268}\)