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.)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0dffadf4-6195-4ecd-8325-0f00263ddf75%2F23121f88-87c9-4f8d-997d-56cf26bb83c3%2Fjpljl07_processed.jpeg&w=3840&q=75)
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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