Here are the null and alternative hypotheses for each situation:

(a) Testing if the spindle diameter has moved away from 5.5 mm:

Since we are checking if the mean diameter is different from the required measurement (5.5 mm), we use a two-tailed test.

• $H_0$: $\mu = 5.5$ (The mean diameter is 5.5 mm)
• $H_a$: $\mu \neq 5.5$ (The mean diameter is different from 5.5 mm)

(b) Testing if prices in Caldwell are higher than the nationwide average price:

Since Harry believes prices in Caldwell are higher than the nationwide average, we use a one-tailed test.

• $H_0$: $\mu = 24.15$ (The mean price in Caldwell is the same as the nationwide average)
• $H_a$: $\mu > 24.15$ (The mean price in Caldwell is higher than the nationwide average)

Would you like further details or have any questions about hypothesis testing?

Here are some related questions to deepen your understanding:

1. How do we choose between a one-tailed and a two-tailed test in hypothesis testing?
2. What are Type I and Type II errors in hypothesis testing?
3. How does sample size impact the outcome of hypothesis testing?
4. Why is it important to specify the standard deviation in hypothesis testing?
5. How would you interpret a p-value in the context of these hypotheses?

Tip: Always determine if you are testing for "greater than," "less than," or "not equal to" when setting up your hypotheses, as this directs the type of test to perform.