Confidence interval for a single mean (σunknown)

To calculate the confidence interval for a single mean when the population standard deviation (σ) is unknown, follow these steps:

1. Collect a sample from the population of interest. The sample should be random and representative.

2. Calculate the sample mean (x̄) and the sample standard deviation (s) from the collected data.

3. Determine the desired level of confidence for the interval. Common choices are 90%, 95%, or 99%.

4. Look up the corresponding critical value (z*) for the chosen confidence level. This value can be found in a standard normal distribution table or calculated using statistical software.

5. Calculate the margin of error (E) using the formula: E = z* * (s / √n), where n is the sample size.

6. Calculate the lower and upper bounds of the confidence interval using the formulas: Lower bound = x̄ - E and Upper bound = x̄ + E.

7. Interpret the confidence interval. This means stating that we are X% confident that the true population mean falls within the calculated interval.

Remember that the confidence interval provides a range of plausible values for the population mean based on the sample data. The larger the sample size and the higher the chosen confidence level, the narrower the interval will be.