Question

During a water shortage, Maryville Water Company randomly sampled residential water meters in order to monitor daily water consumption. On a particular day, a sample of 50 meters showed a sample mean of 240 gallons and a sample standard deviation of 45 gallons. Provide a 90% confidence interval estimate of the population mean water consumption.

Answer 1

The confidence interval for the mean water consumption is obtained using the formula,

(Since the population standard deviation is not known, the t critical value is used to calculate the confidence interval)

where

Sample mean = 240 gallons

Sample standard deviation = 45 gallons

The t critical value is obtained from t distribution table for significance level = 0.10 and degree of freedom = n -1 = 50 - 1 = 49.

Now,

.

The supportive calculations are done in excel. The screenshot is shown below,