Confidence Interval Calculation Example
The average height of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16.
Confidence Interval Formula = ( x̄ – z * ơ / √n) to ( x̄ + z * ơ / √n)
To calculate the confidence interval for the average height of the population, we’ll use the following values from your data:
- Sample mean (x̄) = 1.75 m
- Population variance (σ²) = 0.16, so standard deviation (σ) = √0.16 = 0.4 m
- Sample size (n) = 400
- Confidence level (assuming 95%) → z-value = 1.96 (for a 95% confidence interval)
Now, applying the confidence interval formula:
CI=(xˉ−z⋅σn) to (xˉ+z⋅σn)CI = \left( \bar{x} – z \cdot \frac{\sigma}{\sqrt{n}} \right) \text{ to } \left( \bar{x} + z \cdot \frac{\sigma}{\sqrt{n}} \right)
To calculate the confidence interval for the average height of the population, we’ll use the following values from your data:
- Sample mean (x̄) = 1.75 m
- Population variance (σ²) = 0.16, so standard deviation (σ) = √0.16 = 0.4 m
- Sample size (n) = 400
- Confidence level (assuming 95%) → z-value = 1.96 (for a 95% confidence interval)
Now, applying the confidence interval formula:
CI=(xˉ−z⋅σn) to (xˉ+z⋅σn)CI = \left( \bar{x} – z \cdot \frac{\sigma}{\sqrt{n}} \right) \text{ to } \left( \bar{x} + z \cdot \frac{\sigma}{\sqrt{n}} \right)
To calculate the confidence interval for the average height of the population, we’ll use the following values from your data:
- Sample mean (x̄) = 1.75 m
- Population variance (σ²) = 0.16, so standard deviation (σ) = √0.16 = 0.4 m
- Sample size (n) = 400
- Confidence level (assuming 95%) → z-value = 1.96 (for a 95% confidence interval)
Now, applying the confidence interval formula:
CI=(xˉ−z⋅σn) to (xˉ+z⋅σn)CI = \left( \bar{x} – z \cdot \frac{\sigma}{\sqrt{n}} \right) \text{ to } \left( \bar{x} + z \cdot \frac{\sigma}{\sqrt{n}} \right)
To calculate the confidence interval for the average height of the population, we’ll use the following values from your data:
- Sample mean (x̄) = 1.75 m
- Population variance (σ²) = 0.16, so standard deviation (σ) = √0.16 = 0.4 m
- Sample size (n) = 400
- Confidence level (assuming 95%) → z-value = 1.96 (for a 95% confidence interval)
Confidence Interval Calculation Example
CI=(xˉ−z⋅σn) to (xˉ+z⋅σn)CI = \left( \bar{x} – z \cdot \frac{\sigma}{\sqrt{n}} \right) \text{ to } \left( \bar{x} + z \cdot \frac{\sigma}{\sqrt{n}} \right)
