In countries with a water shortage, converting salt water to potable water is a critical problem. The standard method of water distillation is with a single slope solar still. Several enhanced solar energy water distillation systems were investigated in Applied Solar Energy (Vol. 46, 2010). One new system employs a sun tracking meter and a step-wise basin. The new system was tested over three randomly selected days at a location in Amman, Jordan. The daily amounts of distilled water collected by the new system over the three days were 5.07, 5.45, and 5.21 liters per square meter (l/m²). Suppose it is known that the mean daily amount of distilled water collected by the standard method at the same location in Jordan is μ = 1.4 l/m².

a. Set up the null and alternative hypotheses for determining whether the mean daily amount of distilled water collected by the new system is greater than 1.4.

b. For this test, give a practical interpretation of the value α = .10.

c. Find the mean and standard deviation of the distilled water amounts for the sample of three days. (The data are saved in the DISTILL file.)

d. Use the information from part c to calculate the test statistic.

e. Find the observed significance level (p-value) of the test.

f. State, practically, the appropriate conclusion.

g. Find the value of β for μ_a = 5 l/m²Interpret this value.

h. Find the power of the test for μ_a = 5 l/m². Interpret this value.