Final answer:
Among the given standardized test statistic z-values, z = 2.043 and z = -2.124 fall outside the critical z-value range of ±1.960 for a two-tailed test, indicating the null hypothesis should be rejected for these values.
Step-by-step explanation:
When deciding whether to reject the null hypothesis in hypothesis testing, we compare the standardized test statistic z to the critical z-values. Given a two-tailed test, if the test statistic falls outside of the range of the critical z-values, we reject the null hypothesis.
- (a) z = 1.922: Do not reject the null hypothesis as it is within the range of -1.960 to 1.960.
- (b) z = 2.043: Reject the null hypothesis as it is outside the range and greater than 1.960.
- (c) z = -1.778: Do not reject the null hypothesis as it is within the range of -1.960 to 1.960.
- (d) z = -2.124: Reject the null hypothesis as it is outside the range and less than -1.960.
In summary, for a significance level of 0.05 in a two-tailed test, reject the null hypothesis if the z-value falls outside ±1.960. By comparing the provided z-scores to the critical z-values, we can make knowledgeable decisions on whether to reject or not reject the null hypothesis based on where they fall in relation to the critical range.