When the population standard deviation is know, the confidence interval for the population mean is based on the:
When the population standard deviation is known, the confidence interval for the population mean is based on the Z-distribution
When the population standard deviation is known, the confidence interval for the population mean is based on the Z-distribution.
The Z-distribution is a probability distribution that is standard normal, with a mean of 0 and a standard deviation of 1. It forms the basis for many statistical tests and calculations, including confidence intervals.
The formula for calculating the confidence interval for the population mean, assuming a known population standard deviation, is:
CI = X̄ ± Z * (σ/√n)
Where:
– CI represents the confidence interval
– X̄ is the sample mean
– Z is the z-score corresponding to the desired level of confidence (such as 95% or 99%)
– σ is the known population standard deviation
– n is the sample size
The z-score can be obtained from a Z-table or calculated using statistical software. It represents the number of standard deviations a given value is from the mean.
By using the Z-distribution and the known population standard deviation, we can determine the range within which the true population mean is likely to fall with a certain level of confidence. The confidence interval provides an estimate of the precision of our sample mean in representing the population mean.
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