**Investigating Class Sizes Between Portland and Beaverton School Districts**A school administrator aims to determine if there is a significant difference in the number of students per class for Portland Public School district (group 1) compared to the Beaverton School district (group 2). We assume that the populations are normally distributed but with unequal variances. ### Data Collected:- **Portland School District**: - Sample Size (n1): 28 classes - Sample Mean (x̄1): 36 students per class - Standard Deviation (s1): 5- **Beaverton School District**: - Sample Size (n2): 27 classes - Sample Mean (x̄2): 35 students per class - Standard Deviation (s2): 6### Objective:To find a 90% confidence interval for the difference of the means (µ1 - µ2). Utilize technology to find the critical value with degrees of freedom (df) calculated to be approximately 50.6214. The final interval should be rounded to 4 decimal places.### Confidence Interval Calculation:Use the following formula for the confidence interval of the difference of means with unequal variances:\[ CI = (\bar{x1} - \bar{x2}) \pm t_{\alpha/2, df} \times \sqrt{\frac{s1^2}{n1} + \frac{s2^2}{n2}} \]Where:- \( \bar{x1} \) and \( \bar{x2} \) are the sample means- \( s1 \) and \( s2 \) are the standard deviations- \( n1 \) and \( n2 \) are the sample sizes- \( t_{\alpha/2, df} \) is the critical value from the t-distribution for the specified confidence level and degrees of freedom.Insert the calculated critical value below:\[ < \mu1 - \mu2 < \]-----------------This detailed explanation will help students understand how to compare two means from different groups, accounting for unequal variances, using confidence intervals.

The confidence interval measures the range where the true parameter occurs. It has two parts, they…

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 36 students per class with a standard deviation of 5. A random sample of 27 Beaverton classes found a mean of 35 students per class with a standard deviation of 6. Find a 90% confidence interval in the difference of the means. Use technology to find the critical value using df = 50.6214 and round answers to 4 decimal places.