A school administrator wants to see if there is a difference in the number of students per class for Portland Public School district (group 1) compared to the Beaverton School district (group 2). Assume the populations are normally distributed with unequal variances. A random sample of 28 Portland classes found a mean of 34 students per class with a standard deviation of 2. A random sample of 26 Beaverton classes found a mean of 37 students per class with a standard deviation of 4. Find a 90% confidence interval in the difference of the means. Use technology to find the critical value using df = 36.1505 and round answers to 4 decimal places.

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### Analyzing Student Counts in Different School Districts

#### Objective:
A school administrator wants to determine if there is a difference in the number of students per class between the Portland Public School district (group 1) and the Beaverton School district (group 2). It is assumed that the populations are normally distributed with unequal variances.

#### Study Details:
- **Portland Public School district (Group 1)**:
  - Sample Size: 28 classes
  - Mean: 34 students per class
  - Standard Deviation: 2

- **Beaverton School district (Group 2)**:
  - Sample Size: 26 classes
  - Mean: 37 students per class
  - Standard Deviation: 4

#### Task:
Find a 90% confidence interval for the difference in the means. Use technology to determine the critical value using degrees of freedom (df = 36.1505) and round answers to four decimal places.

#### Calculations:
\[ \text{Enter the bounds for } \mu_1 - \mu_2 \]

\[ \boxed{} < \mu_1 - \mu_2 < \boxed{} \]

#### Explanation of Process:
This involves calculating the confidence interval for the difference in means when dealing with two independent samples with unequal variances. Using technology to find the t-critical value for the given degrees of freedom (df = 36.1505), and applying the appropriate statistical formulas will yield the required confidence interval.

This analysis allows the administrator to make an informed decision regarding the statistical difference between the class sizes in the two school districts.
Transcribed Image Text:### Analyzing Student Counts in Different School Districts #### Objective: A school administrator wants to determine if there is a difference in the number of students per class between the Portland Public School district (group 1) and the Beaverton School district (group 2). It is assumed that the populations are normally distributed with unequal variances. #### Study Details: - **Portland Public School district (Group 1)**: - Sample Size: 28 classes - Mean: 34 students per class - Standard Deviation: 2 - **Beaverton School district (Group 2)**: - Sample Size: 26 classes - Mean: 37 students per class - Standard Deviation: 4 #### Task: Find a 90% confidence interval for the difference in the means. Use technology to determine the critical value using degrees of freedom (df = 36.1505) and round answers to four decimal places. #### Calculations: \[ \text{Enter the bounds for } \mu_1 - \mu_2 \] \[ \boxed{} < \mu_1 - \mu_2 < \boxed{} \] #### Explanation of Process: This involves calculating the confidence interval for the difference in means when dealing with two independent samples with unequal variances. Using technology to find the t-critical value for the given degrees of freedom (df = 36.1505), and applying the appropriate statistical formulas will yield the required confidence interval. This analysis allows the administrator to make an informed decision regarding the statistical difference between the class sizes in the two school districts.
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