Question

An ecologist for the state of Missouri has monitored the mercury level in the groundwater near a large smelting plant. The ecologist took a random sample of 15 area wells and determined the mercury level in these wells. The measurements in mg/m^3 were: 0.99, 1.03, 1.07, 1.07, 1.20, 1.25, 1.35, 1.44, 1.60, 1.61, 1.77, 1.80, 1.87, 2.04, and 2.19. The average of these values is 1.49 and the standard deviation is 0.389 mg/m^3. A court settlement requires that the smelter stop operations if the mercury level in the nearby groundwater has an average of more than 1.25 mg/m^3. The ecologist believes that measurements of mercury concentrations are approximately normally distributed. Conduct a test of hypothesis to see if the average is greater than 1.25mg/m^3.

Answer 1

H₀: = 1.25

H₁: > 1.25

The test statistic t = ()/(s/)

                           = (1.49 - 1.25)/(0.389/)

                           = 2.39

At alpha = 0.05, the critical value is t_0.05,14 = 1.761

Since the test statistic value is greater than the critical value, so we should reject the null hypothesis.

There is sufficient evidence to conclude that the average is greater than 1.25mg/m^3.