John Charleston owns a heating oil delivery company that services 1,540 residences. John would like to estimate the number of customers that have oil storage tanks that are less than 100 gallons in capacity. A random sample of 200 customers found that 48 had an oil tank that was less than 100 gallons. The 99% confidence interval to estimate the proportion of customers with oil tanks less than 100 gallons is ------.

Question

Quizplus · Accepted Answer

The 99% confidence interval for the proportion is calculated using the formula for a proportion confidence interval, which includes the sample proportion, the z-value for the confidence level (which is approximately 2.576 for 99%), and the standard error of the proportion. The sample proportion is 48/200 = 0.24, and the standard error is sqrt((0.24*(1-0.24))/200). Plugging these values into the formula gives an interval that matches choice B, which is wider than the others, reflecting the higher confidence level.

John Charleston Owns a Heating Oil Delivery Company That Services