Final answer:
For the manager's situation, the proper setup for hypothesis testing is H0: μ ≤ 24 and Ha: μ > 24. This right-tailed test will determine if the new bonus plan leads to a sales volume greater than the current mean of 24 automobiles per month.
Step-by-step explanation:
The manager of an automobile dealership wants to test if a new bonus plan will increase sales volume. Currently, the mean sales volume is 24 automobiles per month. To determine the most appropriate null hypothesis (H0) and alternative hypothesis (Ha) for this situation, we need a setup that allows us to test if the sales volume after implementing the plan is greater than the existing mean sales volume.
Therefore, the null hypothesis should state that there is no increase and the alternative hypothesis should represent the possibility of an increase. Given that the current mean is 24, the hypotheses would be:
- H0: μ ≤ 24 (The mean sales volume is less than or equal to 24 automobiles)
- Ha: μ > 24 (The mean sales volume is greater than 24 automobiles)
Here, the null hypothesis sets the baseline that sales have not increased (or stayed the same), while the alternative hypothesis captures the manager's hope that sales will be higher under the new bonus plan. This is a right-tailed test since we are only interested in whether the sales volume has increased and not if it has changed in either direction.