A confidence intervel has a width of 50 units.
If the sample mean is 100,
The lower bound of the intervel is?
To determine the lower bound of the confidence interval, we need to know the level of confidence associated with the interval. The width of the confidence interval alone is not sufficient to calculate the lower bound.
A confidence interval is constructed based on the sample mean, the standard deviation (or standard error), and the level of confidence desired. It provides a range of values within which we are confident the true population parameter lies.
If we have the level of confidence along with the width of the interval, we can calculate the margin of error (half the width of the interval) and then determine the lower bound.
Let's assume a commonly used level of confidence, such as 95%.
1. Start by calculating the margin of error:
- Divide the width of the interval (50 units) by 2 to get the margin of error: 50 / 2 = 25 units.
2. Calculate the lower bound:
- Subtract the margin of error from the sample mean:
100 (sample mean) - 25 (margin of error) = 75 units.
Therefore, if the confidence interval has a width of 50 units, and we assume a 95% confidence level, the lower bound of the interval would be 75 units.