Lessons

- 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

# Confidence Interval for a Population mean, with an Unknown Population Variance

If the population variance is not known, then we do the following change to the above confidence interval formula:

- Substitute the population variance (s) with the sample variance (s)
- Us t-distribution instead of normal distribution
*(explained in the following pages)*

We use t-distribution because the use of sample variance introduces extra uncertainty as s varies from sample to sample.

**Example**

We take a sample of 16 stocks from a large population with a mean return of 5.2% and a standard deviation of 1.2%. The population standard deviation is not known.

Calculate the 95% confidence interval for the population mean.

The confidence interval will be:

The value of *t* is observed from the t-table.