Here are the solutions for the hypothesis testing problem:

(a)
The null hypothesis $H_0$:
$H_0: \mu = 62$

This represents the claim that the mean weight of a healthy 3-month-old colt is 62 kg.

(b)
The alternative hypothesis $H_1$ (testing if the mean weight is less than 62 kg):
$H_1: \mu < 62$

(c)
The alternative hypothesis $H_1$ (testing if the mean weight is greater than 62 kg):
$H_1: \mu > 62$

(d)
The alternative hypothesis $H_1$ (testing if the mean weight is different from 62 kg):
$H_1: \mu \neq 62$

(e)
For each test in parts (b), (c), and (d), the area corresponding to the $P$-value would be:

• (b): Left
• (c): Right
• (d): Both

Thus, the correct answer is: "left; right; both".

Would you like additional clarification or further breakdown of the steps?

5 Related Questions:

1. What is the role of $\alpha$ (significance level) in hypothesis testing?
2. How do you interpret a one-tailed vs. a two-tailed test in hypothesis testing?
3. How do you calculate the $P$-value for a hypothesis test?
4. What does rejecting $H_0$ in favor of $H_1$ signify in statistical terms?
5. Why is it important to correctly determine whether to use a left, right, or two-tailed test?

Tip:

Always sketch a quick graph of the null distribution when performing hypothesis testing. It helps visualize the rejection region and where the $P$-value lies.