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This problem is a hypothesis test for a population mean using a significance level of \( \alpha = 0.01 \).

Here’s how to approach the problem step by step:

### Step 1: Define the hypotheses.
- **Null hypothesis (\( H_0 \))**: The mean weight of one-year-old baby boys is 25 pounds.
  
  \[
  H_0: \mu = 25
  \]
  
- **Alternative hypothesis (\( H_a \))**: The mean weight of one-year-old baby boys is different from 25 pounds.
  
  \[
  H_a: \mu \neq 25
  \]

### Step 2: Collect the given information.
- Sample size (\( n \)) = 332
- Sample mean (\( \bar{x} \)) = 25.5 pounds
- Sample standard deviation (\( s \)) = 5.3 pounds
- Significance level (\( \alpha \)) = 0.01

### Step 3: Compute the test statistic.
Since we know the sample size and standard deviation, we use the **t-test for a single population mean**:

\[
t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]

Where:
- \( \bar{x} \) = 25.5 pounds (sample mean),
- \( \mu_0 \) = 25 pounds (claimed mean),
- \( s \) = 5.3 pounds (sample standard deviation),
- \( n \) = 332 (sample size).

Let’s calculate this:

\[
t = \frac{25.5 - 25}{\frac{5.3}{\sqrt{332}}}
\]

### Step 4: Determine the P-value.
You can use the TI-84 Plus calculator to find the **P-value** by entering the test statistic and degrees of freedom \( (df = n - 1 = 332 - 1 = 331) \).

### Step 5: Conclusion.
- If the **P-value** is less than \( \alpha = 0.01 \), you reject the null hypothesis and conclude that there is convincing evidence that the mean weight differs from 25 pounds.
- If the **P-value** is greater than \( \alpha = 0.01 \), you fail to reject the null hypothesis, meaning there is no convincing evidence against the claim.

Would you like me to compute the exact test statistic and P-value for you?

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Here are 5 related questions:
1. How do you calculate a P-value for a two-tailed test manually?
2. What are the differences between a t-test and a z-test?
3. How does changing the significance level \( \alpha \) affect hypothesis testing results?
4. What are degrees of freedom in the context of a t-test, and how do they affect the test?
5. Why do we use the sample standard deviation instead of the population standard deviation?

**Tip:** Always ensure you choose the correct tails for your hypothesis test—this affects the critical value and decision rule.

The National Health Statistics Reports described a study in which a sample of 332 one-year-old baby boys were weighed. Their mean weight was 25.5 pounds with standard deviation 5.3 pounds. A pediatrician claims that the mean weight of one-year-old boys differs from 25 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the α = 0.01 level of significance and the P-value method with the TI-84 Plus calculator.

Learn how to perform hypothesis testing using a significance level of α = 0.01. This problem focuses on comparing the mean weight of one-year-old baby boys to a standard weight of 25 pounds. Key concepts include the P-value method and a t-test calculation, with sample data and TI-84 Plus calculator instructions provided.

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