Which of the following is the width of the confidence interval for the population mean?
Question
Which of the following is the width of the confidence interval for the population mean?
Solution
The width of the confidence interval for the population mean is calculated as:
Width = Upper Limit - Lower Limit
The upper and lower limits of a confidence interval are typically calculated as:
Upper Limit = Sample Mean + (ZStandard Error) Lower Limit = Sample Mean - (ZStandard Error)
Where:
- Z is the Z-score, which corresponds to the desired level of confidence (for example, a Z-score of 1.96 is used for a 95% confidence interval), and
- Standard Error is the standard deviation of the sample mean, calculated as the standard deviation divided by the square root of the sample size.
So, the width of the confidence interval can also be calculated as:
Width = 2 * Z * Standard Error
This is because (Z*Standard Error) is the amount added to and subtracted from the sample mean to find the upper and lower limits, respectively.
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