Independent random samples from normal populations produced the results shown in the table to the right. Complete parts a through d below. a. Calculate the pooled estimate of o s = (Round to four decimal places as needed.) Sample 1 2.2 1.2 3.3 1.1 2.9 Sample 2 2.9 3.3 2.9 3.4
Independent random samples from normal populations produced the results shown in the table to the right. Complete parts a through d below. a. Calculate the pooled estimate of o s = (Round to four decimal places as needed.) Sample 1 2.2 1.2 3.3 1.1 2.9 Sample 2 2.9 3.3 2.9 3.4
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![### Statistical Analysis of Independent Random Samples
Independent random samples from normal populations produced the following results. Complete parts (a) through (d) below.
#### Data Table:
| Sample 1 | Sample 2 |
| --- | --- |
| 2.2 | 2.9 |
| 1.2 | 3.3 |
| 3.3 | 2.9 |
| 1.1 | 3.4 |
| - | - |
### Task:
**a. Calculate the pooled estimate of \(\sigma^2\).**
\[ s_p^2 = \boxed{\phantom{4.0000}} \]
(Round to four decimal places as needed.)
This section will help students understand the process of calculating the pooled estimate of variance (\(\sigma^2\)) using the given data from two independent samples. The pooled variance is a method that provides a single estimate of variance by combining data from both samples.
1. **Sample Data:**
- *Sample 1:* 2.2, 1.2, 3.3, 1.1
- *Sample 2:* 2.9, 3.3, 2.9, 3.4
2. **Calculation Steps:**
- Calculate the sample means (\(\bar{x}_1\) and \(\bar{x}_2\)).
- Compute the sum of squared deviations from the mean for each sample.
- Sum the squared deviations for both samples.
- Divide the total sum by the degrees of freedom (total number of observations - 2).
By following these steps, students can accurately determine the pooled estimate of the population variance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdd081ff-4988-4514-ab5d-41964c228e08%2Fb2711951-c023-4532-9c99-290e682916d1%2Fw266mr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Independent Random Samples
Independent random samples from normal populations produced the following results. Complete parts (a) through (d) below.
#### Data Table:
| Sample 1 | Sample 2 |
| --- | --- |
| 2.2 | 2.9 |
| 1.2 | 3.3 |
| 3.3 | 2.9 |
| 1.1 | 3.4 |
| - | - |
### Task:
**a. Calculate the pooled estimate of \(\sigma^2\).**
\[ s_p^2 = \boxed{\phantom{4.0000}} \]
(Round to four decimal places as needed.)
This section will help students understand the process of calculating the pooled estimate of variance (\(\sigma^2\)) using the given data from two independent samples. The pooled variance is a method that provides a single estimate of variance by combining data from both samples.
1. **Sample Data:**
- *Sample 1:* 2.2, 1.2, 3.3, 1.1
- *Sample 2:* 2.9, 3.3, 2.9, 3.4
2. **Calculation Steps:**
- Calculate the sample means (\(\bar{x}_1\) and \(\bar{x}_2\)).
- Compute the sum of squared deviations from the mean for each sample.
- Sum the squared deviations for both samples.
- Divide the total sum by the degrees of freedom (total number of observations - 2).
By following these steps, students can accurately determine the pooled estimate of the population variance.
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