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Confidence Intervals for the Population Mean

幫考網校 2020-08-07 14:36:28
A confidence interval for the population mean is a range of values that is likely to contain the true population mean with a certain level of confidence. The level of confidence is typically expressed as a percentage, such as 95% or 99%.

To calculate a confidence interval for the population mean, you need to know the sample mean, sample standard deviation, sample size, and the level of confidence. The formula for calculating the confidence interval is:

Confidence interval = sample mean ± (z-score x standard error)

where the z-score is based on the level of confidence and the standard error is calculated as:

Standard error = sample standard deviation / square root of sample size

For example, if you have a sample of 50 students and their average test score is 75 with a standard deviation of 10, and you want to calculate a 95% confidence interval for the population mean, the calculation would be:

Standard error = 10 / sqrt(50) = 1.41

The z-score for a 95% confidence level is 1.96 (from a standard normal distribution table).

Confidence interval = 75 ± (1.96 x 1.41) = 75 ± 2.76

Therefore, the 95% confidence interval for the population mean is between 72.24 and 77.76. This means that we are 95% confident that the true population mean falls within this range.
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