When a z score falls outside the region of rejection, we conclude that there is not enough evidence to reject the null hypothesis. This typically means that the sample data we have does not show a statistically significant effect or difference when compared to the null hypothesis.
The region of rejection is determined by the significance level (alpha) set for the test, typically 0.05, which corresponds to the z scores beyond approximately ±1.96 for a two-tailed test. If our calculated z score falls within the boundaries of -1.96 and +1.96, it suggests that any observed differences could easily be attributed to chance variation rather than a true effect.
In other words, failing to fall in the region of rejection indicates that while we have some data, it does not provide sufficient evidence to conclude that the alternative hypothesis is true. Thus, we would maintain our assumption that the null hypothesis is valid based on the given level of significance.