Confidence Interval for a Population mean, with a known Population Variance

We have the following assumptions:

  • Population variance σ2 is known
  • Population is normally distributed

Under these assumptions, the confidence interval estimate will be given as follows:

Example

Let’s take an example to compute this.

We take a sample of 16 stocks from a large population with a mean return of 5.2%. We know that the population standard deviation is 1.5%.

Calculate the 95% confidence interval for the population mean.

For 95% confidence interval, zα/2 = 1.96

The confidence interval will be:

We are 95% confidence that the true mean is between 4.465% an­­d 5.935%.

z is obtained from the standard normal distribution table as shown below. F(Z) value is 0.025 at z = -1.96 and F(Z) value is 0.9750 at z = 1.96.

The most commonly used confidence intervals are 90%, 95%, 99% and 99.9%. The z values are given below.

Confidence LevelZa/2 Value
90%1.645
95%1.96
99%2.58
99.9%3.27

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