Answer:
1. The point estimate for population mean is 25.
2)
![\text{Margin of error} = \pm 3](https://tex.z-dn.net/?f=%5Ctext%7BMargin%20of%20error%7D%20%3D%20%5Cpm%203)
Step-by-step explanation:
We are given the following information in the question:
Confidence interval: (22,28)
Confidence interval is calculated as:
![\text{Sample mean }\pm \text{ Margin of error}](https://tex.z-dn.net/?f=%5Ctext%7BSample%20mean%20%7D%5Cpm%20%5Ctext%7B%20Margin%20of%20error%7D)
Thus, we can write the equations:
![\bar{x} - \text{Margin of error} = 22\\\bar{x} + \text{Margin of error} = 28](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20-%20%5Ctext%7BMargin%20of%20error%7D%20%3D%2022%5C%5C%5Cbar%7Bx%7D%20%2B%20%5Ctext%7BMargin%20of%20error%7D%20%3D%2028)
1) The point estimate of the population mean
To calculate the point estimate of the population mean we solve the two equations, to find the sample mean
Adding the two equations we get:
![2\bar{x} = 22+ 28 = 50\\\bar{x} = 25](https://tex.z-dn.net/?f=2%5Cbar%7Bx%7D%20%3D%2022%2B%2028%20%3D%2050%5C%5C%5Cbar%7Bx%7D%20%3D%2025)
Thus, the point estimate for population mean is 25.
2) The margin of error for the confidence interval
Putting the values from the equation, we get:
![\text{Margin of error} = 28 - 25 = 3](https://tex.z-dn.net/?f=%5Ctext%7BMargin%20of%20error%7D%20%3D%2028%20-%2025%20%3D%203)
Thus, the margin of error f the given confidence interval is
![\text{Margin of error} = \pm 3](https://tex.z-dn.net/?f=%5Ctext%7BMargin%20of%20error%7D%20%3D%20%5Cpm%203)