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?

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.