# 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 Level | Za/2 Value |

90% | 1.645 |

95% | 1.96 |

99% | 2.58 |

99.9% | 3.27 |

- Simple Random Sampling and Sampling Distribution
- Sampling Error
- Stratified Random Sampling
- Time Series and Cross Sectional Data
- Central Limit Theorem
- Standard Error of the Sample Mean
- Parameter Estimation
- Point Estimates
- Confidence Interval Estimates
- Confidence Interval for a Population mean, with a known Population Variance
- Confidence Interval for a Population mean, with an Unknown Population Variance
- Confidence Interval for a Population Mean, when the Distribution is Non-normal
- Student’s t Distribution
- How to Read Student’s t Table
- Biases in Sampling

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