Question

A random sample of 40 households has an average water consumption of 29 cubic meters per month with a standard deviation of 8 cubic meters. Give the 90% confidence interval for the mean usage of water per month.

Answer 1

The formula to calculate a confidence interval for a population mean is as follows:

$CI=\bar{x}\pm z\cdot\cfrac{\sigma}{\sqrt{n}},$

where:

• $\bar{x}=29$ : sample mean
• z:  the chosen z-value, for a 90% confidence interval z = 1.645
• $\sigma=8$ :  sample standard deviation
• n = 40:  sample size.

So,

$CI=29 \pm 1.645\cdot\cfrac{8}{\sqrt{40}}=\\ =29\pm2. 08=(26.92, 31.08).$