Question

QUESTION 11 In Jefferson county, the mean water usage per household for the month of January 2018 was .060 acre-feet (an acre-foot is the amount of water necessary to cover one acre to a depth of one foot.) This figure is based on the usage of all households in the county during that month. In January 2019, a random sample of 50 homes was selected, and water usage was recorded for each home in the sample. The mean water usage per household in the sample was .054 acre-feet with a standard deviation (s) of .016 acre-feet. The county would like to know whether the data support the claim that mean January water usage has declined. Conduct an appropriate statistical hypothesis test using a 0.01 significance level. Find the associated the P-value to four decimal places.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 0.06
Alternative Hypothesis: μ < 0.06

Rejection Region
This is left tailed test, for α = 0.01 and df = 49
Critical value of t is -2.405.
Hence reject H0 if t < -2.405

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (0.054 - 0.06)/(0.016/sqrt(50))
t = -2.652

P-value Approach
P-value = 0.0054
As P-value < 0.01, reject the null hypothesis.