9.2.9-1 Independent random samples from normal populations produced the results shown in the table to the right. Complete parts a through d below. Sample 2 Sample 1 3.2 2.5 2.5 3.1 3.1 3.6 1.8 3.1 a. Calculate the pooled estimate of o (Round to four decimal places as needed.)

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### Statistical Analysis of Independent Random Samples

**Score:** 0 of 1 pt

**Question No:** 9.2.9-T

Independent random samples from normal populations produced the results shown in the table below. Complete parts (a) through (d) below.

#### Data Table:

|        | Sample 1 | Sample 2 |
|--------|----------|----------|
| Values |    3.2   |    3.8   |
|        |    2.5   |    3.1   |
|        |    2.5   |    3.1   |
|        |    1.8   |    3.6   |
|        |    3.1   |          |

#### Questions:

**a. Calculate the pooled estimate of σ².**

\[ s_p^2 = \]

*(Round to four decimal places as needed.)*

---

This section involves calculating the pooled variance \( s_p^2 \) from the given samples. The formula for the pooled variance is:

\[ s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{(n_1 + n_2 - 2)} \]

Where:
- \( s_1^2 \) and \( s_2^2 \) are the sample variances.
- \( n_1 \) and \( n_2 \) are the sample sizes.

Feel free to use a calculator to find the sample variances and sizes before computing the pooled variance. Make sure to round your final answer to four decimal places.

### Understanding the Data:
- **Sample 1** consists of the values: 3.2, 2.5, 2.5, 1.8, and 3.1.
- **Sample 2** consists of the values: 3.8, 3.1, 3.1, and 3.6.

These measurements are being used to estimate the pooled variance from two different normal populations.

For further details, consult your statistics textbook or seek help from a teacher or mentor who can guide you through the calculation steps for pooled variance.
Transcribed Image Text:### Statistical Analysis of Independent Random Samples **Score:** 0 of 1 pt **Question No:** 9.2.9-T Independent random samples from normal populations produced the results shown in the table below. Complete parts (a) through (d) below. #### Data Table: | | Sample 1 | Sample 2 | |--------|----------|----------| | Values | 3.2 | 3.8 | | | 2.5 | 3.1 | | | 2.5 | 3.1 | | | 1.8 | 3.6 | | | 3.1 | | #### Questions: **a. Calculate the pooled estimate of σ².** \[ s_p^2 = \] *(Round to four decimal places as needed.)* --- This section involves calculating the pooled variance \( s_p^2 \) from the given samples. The formula for the pooled variance is: \[ s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{(n_1 + n_2 - 2)} \] Where: - \( s_1^2 \) and \( s_2^2 \) are the sample variances. - \( n_1 \) and \( n_2 \) are the sample sizes. Feel free to use a calculator to find the sample variances and sizes before computing the pooled variance. Make sure to round your final answer to four decimal places. ### Understanding the Data: - **Sample 1** consists of the values: 3.2, 2.5, 2.5, 1.8, and 3.1. - **Sample 2** consists of the values: 3.8, 3.1, 3.1, and 3.6. These measurements are being used to estimate the pooled variance from two different normal populations. For further details, consult your statistics textbook or seek help from a teacher or mentor who can guide you through the calculation steps for pooled variance.
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