Babies: 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 5 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the a=0.01 level of significance. Part 1 of 5 State the appropriate null and alternate hypotheses. V 5 %3D H1:0 > 5 This hypothesis test is a right-tailed V test. Part 2 of 5 Find the critical value. Round the answer to three decimal places. For a= 0.01 , the critical value is 42.980

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**Babies: Statistical Analysis on One-Year-Old Girls' Weights**

**Overview:**
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 5 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the α = 0.01 level of significance.

**Part 1 of 5: Hypothesis Testing**

State the appropriate null and alternate hypotheses:

- Null Hypothesis (\(H_0\)): \(\sigma = 5\)
- Alternate Hypothesis (\(H_1\)): \(\sigma > 5\)

This hypothesis test is a **right-tailed** test.

**Part 2 of 5: Determine the Critical Value**

Find the critical value. Round the answer to three decimal places.

For \(\alpha = 0.01\), the critical value is **42.980**.

*Illustration:* A progress bar shows "Part: 2 / 5."

**Part 3 of 5: Compute the Test Statistic**

Compute the test statistic. Round the answer to three decimal places.

- Computed Test Statistic (\(\chi^2\)): [Provide the answer]

**Explanation:**
- **Hypotheses:** It outlines that the test is examining whether the population standard deviation of weights is greater than 5 pounds.
- **Critical Value:** The given critical value to reject the null hypothesis is provided.
- **Test Statistic Calculation:** This would involve a computation based on the given sample data.

Note: Parts 4 and 5 are not displayed in the image and are assumed to be subsequent steps in hypothesis testing, potentially involving the actual computation of the test statistic, decision rule, and conclusion. This example explains the initial steps and how they are structured in statistical analysis.
Transcribed Image Text:**Babies: Statistical Analysis on One-Year-Old Girls' Weights** **Overview:** 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 5 pounds. Do the data provide convincing evidence that the pediatrician's claim is true? Use the α = 0.01 level of significance. **Part 1 of 5: Hypothesis Testing** State the appropriate null and alternate hypotheses: - Null Hypothesis (\(H_0\)): \(\sigma = 5\) - Alternate Hypothesis (\(H_1\)): \(\sigma > 5\) This hypothesis test is a **right-tailed** test. **Part 2 of 5: Determine the Critical Value** Find the critical value. Round the answer to three decimal places. For \(\alpha = 0.01\), the critical value is **42.980**. *Illustration:* A progress bar shows "Part: 2 / 5." **Part 3 of 5: Compute the Test Statistic** Compute the test statistic. Round the answer to three decimal places. - Computed Test Statistic (\(\chi^2\)): [Provide the answer] **Explanation:** - **Hypotheses:** It outlines that the test is examining whether the population standard deviation of weights is greater than 5 pounds. - **Critical Value:** The given critical value to reject the null hypothesis is provided. - **Test Statistic Calculation:** This would involve a computation based on the given sample data. Note: Parts 4 and 5 are not displayed in the image and are assumed to be subsequent steps in hypothesis testing, potentially involving the actual computation of the test statistic, decision rule, and conclusion. This example explains the initial steps and how they are structured in statistical analysis.
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