In your case, you have conducted a right-tailed Z-test and found a test statistic of Z = 0.05. A right-tailed test is a statistical test in which the area of rejection is on the right side of the sampling distribution.

The level of significance (α) is the probability of rejecting the null hypothesis when it is true. In your case, the level of significance is 5% (0.05).

Therefore, at a 5% level of significance, the correct decision would be to fail to reject the null hypothesis. This means that there is not enough evidence to support the alternative hypothesis.

To make a decision in hypothesis testing, we compare the test statistic (Z-score) to the critical value at the given level of significance.

A Z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is a Z-score (Z).