Question

A city planner wants to estimate, with a 99% confidence level, the average monthly residential water usage in the city. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 387.40 gallons. How large a sample should be selected so that the estimate for the average monthly residential water usage in this city is within 110 gallons of the population mean?

Round your answers to the nearest integer.

n=

Answer 1

Answer: 82

Step-by-step explanation:

The formula to find the sample size is given by :-

$n= (\dfrac{z^*\cdot \sigma}{E})^2$

, where E = Margin of error.

$\sigma$ = Population standard deviation for the prior study.

As per given , we have

$\sigma=387.40$ gallons.

Margin of error : E= 110 gallons

Critical value for 99% confidence level = z* = 2.576

Then, the required sample size : $n= (\dfrac{(2.576)\cdot (387.40)}{110})^2$

$n= (9.07220363636)^2\approx82$  {Rounded to the nearest integer.}

Hence, the minimum sample size = 82