When the following hypotheses are being tested at a level of significance of
aH0: m 100
Ha: m < 100
the null hypothesis will be rejected if the test statistic Z is
a. >Z
b. >Z
c. <Z
d. <100
You are lacking information on variability and level of significance used (e.g., P ≤ .05, P ≤ .01).
It would also help if you proofread your questions before you posted them. Choices a and b are identical.
To determine if the null hypothesis should be rejected or not, we need to compare the test statistic, Z, with a critical value.
In this case, since the alternative hypothesis (Ha) states that the population mean (m) is less than 100, we are conducting a left-tailed test.
The critical value for a left-tailed test is found in the left tail of the standard normal distribution (Z-distribution). The critical value represents the point at which we can reject the null hypothesis.
Since the question does not provide a specific critical value, we assume that Z is the test statistic and represents the standard normal distribution.
Therefore, the null hypothesis will be rejected if the test statistic Z is LESS THAN the critical value.
So, the correct answer is c. <Z