Let's analyze the question from the image:

Problem Breakdown:

A study with 332 one-year-old baby boys has a mean weight of 25.5 pounds and a standard deviation of 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys differs from 25 pounds. We are tasked to:

1. Formulate the null and alternative hypotheses.
2. Identify the type of test.

Step 1: Formulating the Hypotheses

• Null Hypothesis (H₀): The null hypothesis represents the idea that there is no significant difference between the mean weight observed in the sample and the hypothesized mean (25 pounds). Hence, $H_0: \mu = 25 \, \text{pounds}$

• Alternative Hypothesis (H₁): The alternative hypothesis is based on the claim that the mean weight differs from 25 pounds, implying a two-tailed test. Hence, $H_1: \mu \neq 25 \, \text{pounds}$

Step 2: Identifying the Type of Test

Since the claim is that the mean weight differs from a specific value (25 pounds), we will use a two-tailed test.

Answer:

• $H_0: \mu = 25$
• $H_1: \mu \neq 25$
• This is a two-tailed test.

Let me know if you want details about further steps like conducting the test or if you have more questions!

Relative Questions:

1. How do you calculate the test statistic for this hypothesis test?
2. What is the significance of a two-tailed test in hypothesis testing?
3. How do we interpret the P-value in the context of this test?
4. What assumptions must be met to perform a hypothesis test on means?
5. How does the sample size influence the outcome of hypothesis tests?

Tip:

In a two-tailed test, the alternative hypothesis suggests the parameter could either be less than or greater than the hypothesized value, making both extremes critical for rejection of the null hypothesis.