Final answer:
The null hypothesis H0: μ ≥ 100 will be rejected in favor of the alternative hypothesis Ha: μ < 100 at a significance level α if the test statistic z is less than the negative critical value –zα, indicating a left-tailed test.
Step-by-step explanation:
When testing the hypotheses H0: μ ≥ 100 and Ha: μ < 100 at a level of significance of α, we must compare our test statistic to critical values from the appropriate statistical distribution. Since this is a left-tailed test (as indicated by the 'less than' symbol in Ha), the null hypothesis will be rejected if the test statistic z is less than the negative critical value –zα. This critical value corresponds to the cutoff point where the left-tail area equals the significance level α.
For example, if α is 0.05, you would look up the z-value that corresponds to the left-tail area of 0.05 in the z-table. If your calculated z-value is less than this critical value (e.g., if the critical z-value is -1.645 for α = 0.05 and your z is lesser like -1.70), you would reject the null hypothesis, indicating that there is sufficient statistical evidence to support the alternative hypothesis Ha: μ < 100.