5.2 Two-tailed test

For a two-tailed test, we need to adjust our approach slightly. We still use NORM.S.INV(), but we must account for the probability being split between two tails.

Let us use the same example (α = 5%). In a two-tailed test, we split our α evenly between the two tails..

The lower tail z-value would correspond to the 2.5% of the distribution, so you would use:

• =NORM.S.INV(0.025)

This gives approximately -1.96.

The upper tail z-value would correspond to the 97.5% of the distribution, so you would use:

• =NORM.S.INV(0.975)

This gives us a z critical value of approximately 1.96.

Together, the z critical values are: ±1.96

In practice, this means we reject the null hypothesis if our calculated test statistic is either smaller than -1.96 or larger than 1.96. These values create our "rejection region" - the areas in the tails of the distribution where the evidence against the null hypothesis is strong enough to warrant rejection.

To interpret your results:

• If your test statistic falls between -1.96 and 1.96, you fail to reject the null hypothesis.
• If your test statistic is less than -1.96 or greater than 1.96, you reject the null hypothesis.