A sample of birth weights of 31 girls was taken. Below are the results (in g): 3201.2 2480.6 3120 2879.8 3573.2 3477.2 3827.7 3440.1 3101.9 3399.8 3546.8 3696.8 3047.6 3301.6 3447.4 3179.5 3442.7 3435.8 3623.3 3189.1 3707.5 2880.7 2878.4 3173.5 3264 3438.1 3192.4 3493 4456.1 3570.4 3557.5 I=3355.6 g 8 = 356.01 g Use a 10% significance level to test the claim that the standard deviation of birth weights of girls is different from the standard deviation of birth weights of boys, which is 460 g. Round all answers to 3 decimal places if possible.

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I need to compute the test statistic, critical values, and p-value I know the test is two tailed, I just can't work out how to do it..

**Analysis of Birth Weights of Girls**

A study was conducted to understand the birth weights of 31 girls. The collected data, presented in grams (g), is as follows:

| 3201.2 | 2480.6 | 3120.0 | 2879.8 | 3438.1 |
|--------|--------|--------|--------|--------|
| 3573.2 | 3477.2 | 3827.7 | 3440.1 | 3192.4 |
| 3101.9 | 3399.8 | 3546.8 | 3696.8 | 3493.0 |
| 3047.6 | 3301.6 | 3447.4 | 3179.5 | 4456.1 |
| 3442.7 | 3435.8 | 3623.3 | 3189.1 | 3570.4 |
| 3707.5 | 2880.7 | 2878.4 | 3173.5 | 3557.5 |
| 3264.0 |        |        |        |        |

### Descriptive Statistics

From the data collected:
- The mean birth weight ( \( \bar{x} \) ) is calculated as 3355.6 g.
- The sample standard deviation ( \( s \) ) is calculated as 356.01 g.

### Hypothesis Testing

We aim to test the claim that the standard deviation of birth weights for girls is different from the known standard deviation of birth weights for boys, which is 460 g. This will be evaluated using a significance level of 10%.

**Hypotheses:**
- Null Hypothesis ( \( H_0 \) ): \( \sigma = 460 \) g
- Alternative Hypothesis ( \( H_a \) ): \( \sigma \neq 460 \) g

We will conduct a hypothesis test using the chi-squared distribution to determine whether to reject the null hypothesis based on the given data.

### Instructions

1. **Calculate Test Statistic**: Use the chi-squared test statistic for variance:

\[ \chi^2 = \frac{(n - 1) s^2}{\sigma^2} \]

Where:
- \( n \) = sample size (31)
- \( s \) = sample standard deviation (
Transcribed Image Text:**Analysis of Birth Weights of Girls** A study was conducted to understand the birth weights of 31 girls. The collected data, presented in grams (g), is as follows: | 3201.2 | 2480.6 | 3120.0 | 2879.8 | 3438.1 | |--------|--------|--------|--------|--------| | 3573.2 | 3477.2 | 3827.7 | 3440.1 | 3192.4 | | 3101.9 | 3399.8 | 3546.8 | 3696.8 | 3493.0 | | 3047.6 | 3301.6 | 3447.4 | 3179.5 | 4456.1 | | 3442.7 | 3435.8 | 3623.3 | 3189.1 | 3570.4 | | 3707.5 | 2880.7 | 2878.4 | 3173.5 | 3557.5 | | 3264.0 | | | | | ### Descriptive Statistics From the data collected: - The mean birth weight ( \( \bar{x} \) ) is calculated as 3355.6 g. - The sample standard deviation ( \( s \) ) is calculated as 356.01 g. ### Hypothesis Testing We aim to test the claim that the standard deviation of birth weights for girls is different from the known standard deviation of birth weights for boys, which is 460 g. This will be evaluated using a significance level of 10%. **Hypotheses:** - Null Hypothesis ( \( H_0 \) ): \( \sigma = 460 \) g - Alternative Hypothesis ( \( H_a \) ): \( \sigma \neq 460 \) g We will conduct a hypothesis test using the chi-squared distribution to determine whether to reject the null hypothesis based on the given data. ### Instructions 1. **Calculate Test Statistic**: Use the chi-squared test statistic for variance: \[ \chi^2 = \frac{(n - 1) s^2}{\sigma^2} \] Where: - \( n \) = sample size (31) - \( s \) = sample standard deviation (
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