For a two-tail Z test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the test statistic is

A two-tail Z test is used when you are testing for the possibility of the relationship in both directions. The 0.05 level of significance means that there is a 5% chance that you will reject the null hypothesis when it is true.

Here are the steps to determine the value of the test statistic at which the null hypothesis will be rejected:

1. Identify the level of significance: In this case, it is 0.05.

2. Since it's a two-tail test, you need to divide the level of significance by 2. This is because the two-tail test allocates some of the alpha to the right tail and some to the left tail of the distribution. So, 0.05/2 = 0.025.

3. Look up the Z score that corresponds to this divided significance level (0.025) in a standard normal distribution table or use a Z score calculator. The Z score that corresponds to a cumulative probability of 0.025 (in the left tail) and 0.975 (in the right tail) is approximately -1.96 and +1.96, respectively.

4. Therefore, the null hypothesis will be rejected if the value of the test statistic is less than -1.96 or greater than +1.96.

In other words, if the Z score is beyond the critical values of -1.96 and +1.96, we reject the null hypothesis.