Final answer:
The correct null hypothesis (H0) is that the mean diameter is 5 mm, and the alternative hypothesis (Ha) is that the mean diameter is not equal to 5 mm, as the manufacturer is concerned with both possibilities of it being too small or too large. Therefore, option A is correct stating H0: Mean = 5 and Ha: Mean is not equal to 5.
Step-by-step explanation:
The question you've asked pertains to hypothesis testing, which is a method in statistics to decide whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Here, a manufacturer is testing the mean diameter of motor spindles to ensure it's 5 mm.
The null hypothesis (H0) is a statement that there is no effect or no difference, and it is assumed to be true until evidence indicates otherwise. For this scenario, since the spindle is supposed to be 5 mm, the null hypothesis would be that the mean diameter of the spindles is equal to 5 mm.
The alternative hypothesis (Ha) is what you would conclude if the evidence suggests that the null hypothesis isn't true. In this case, you are concerned with the mean diameter being either too small or too large, which indicates a two-sided alternative. Therefore, the alternative hypothesis is that the mean diameter is not equal to 5 mm.
The correct choice, considering the two-sided nature of the alternative (the manufacturer is concerned with the spindle being both too small or too large), is: H0: Mean = 5 and Ha: Mean is not equal to 5. Option A reflects this correctly.