what is the difference between Calculating interval estimation for a single population mean in case 1 and case 3
In case 1, the population standard deviation is known, whereas in case 3, the population standard deviation is unknown.
Case 1:
- When calculating interval estimation for a single population mean, known standard deviation, the formula used is:
- Confidence interval = sample mean ± (critical value * standard deviation/square root of sample size)
- The critical value is determined based on the desired confidence level.
- This case assumes that the population standard deviation is known, and the formula uses that known value.
Case 3:
- When calculating interval estimation for a single population mean, unknown standard deviation, the formula used is:
- Confidence interval = sample mean ± (critical value * sample standard deviation/square root of sample size)
- The critical value and sample standard deviation are both determined based on the sample data.
- This case assumes that the population standard deviation is unknown, so the formula uses the sample standard deviation as an estimate for it.
The primary difference between the two cases is whether the population standard deviation is known or unknown. In case 1, the formula incorporates the known population standard deviation, while in case 3, the formula uses the sample standard deviation as an estimate for the unknown population standard deviation.