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This problem is asking for a hypothesis test to evaluate the claim of a pediatrician regarding the standard deviation of weights of one-year-old girls. Specifically, it is about testing whether the standard deviation is greater than 3 pounds. 

Let's break down the steps to correctly form the hypotheses and interpret the test type:

### Part 1: Null and Alternative Hypotheses

- **Null Hypothesis \( H_0 \):** This represents the status quo or the assumption that the pediatrician's claim is *not* true.
  - Here, the null hypothesis would state that the standard deviation is **equal to** 3 pounds.
  - \( H_0: \sigma = 3 \)

- **Alternative Hypothesis \( H_1 \):** This is the claim you are testing for, which states that the pediatrician claims the standard deviation is **greater than** 3 pounds.
  - \( H_1: \sigma > 3 \)

### Part 2: Type of Test

Since this is a hypothesis test for a population standard deviation, and we're testing whether it is **greater than** a given value, this would be a **right-tailed chi-square test** for the population variance (standard deviation squared).

So, your answers should be:
- **Null Hypothesis \( H_0: \sigma = 3 \)**
- **Alternative Hypothesis \( H_1: \sigma > 3 \)**
- **This is a right-tailed test**.

Would you like more details or help with any other parts of this problem?

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Here are 5 related questions to expand your understanding:
1. How do you calculate the test statistic for a chi-square test for standard deviation?
2. What assumptions need to be met for the chi-square test to be valid?
3. What is the formula for the chi-square test statistic in hypothesis testing for standard deviation?
4. How does the level of significance \( \alpha \) impact the rejection region in a hypothesis test?
5. What is the difference between a one-tailed and a two-tailed test in hypothesis testing?

**Tip:** In hypothesis testing, always clearly define the null and alternative hypotheses before starting your calculations, as this sets the foundation for the rest of the test.

A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of 4.3 pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is greater than 3 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the α = 0.01 level of significance.

Learn how to perform a hypothesis test for a standard deviation claim using a chi-square test. This example evaluates the pediatrician's claim that the standard deviation of weights of one-year-old girls is greater than 3 pounds at a 0.01 significance level. Detailed solution includes setting up null and alternative hypotheses and determining the test type.

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