194. Confidence Intervals

Range within which we can be confident that the true value (population parameter) lies, based on the sample data

1. Known population standard deviation ($𝜎$):

Where:

• $\overline{𝑥}$: sample mean
• $𝑧$: z-score corresponding to the desired confidence level
• $𝜎$: population standard deviation
• $𝑛$: sample size

2. Unknown population standard deviation ($𝜎$):

Where:

• $\overline{𝑥}$: sample mean
• $𝑡$: critical value from t-distribution
• $𝑠$: sample standard deviation
• $𝑛$: sample size