Question

According to data from the Environmental Protection Agency, the average daily water consumption for a household of four people in the United States is approximately 243 gallons. (Source: http://www.catskillcenter.org/programs/csp/H20/Lesson3/house3.htm) Suppose a state agency plans to test this claim using an alpha level equal to 0.05 and a random sample of 100 households with four people. What is the lower critical value in terms of gallons if the population standard deviation is known to be 40 gallons?

236.42

249.58

235.16 gallons

250.84

Answer 1

The provided sample mean is Xbar=243 and the population standard deviation is σ=40.

The size of the sample is n=100 and the required confidence level is 95%.

Based on the provided information, the critical z-value for α=0.05 is zc​=1.96.

(calculated using normal table)

The 95% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean μ is

\

So the lower critical value is 235.16 gallon