Contamination of mine soils in China is a serious environmental problem. The article "Heavy Metal Contamination in Soils and Phytoaccumulation in a Manganese Mine Wasteland, South China" (Air,
Soil, and Water Res., 2008: 31-41) reported that, for a sample of 3 soil specimens from a certain restored mining area, the sample mean concentration of Total Cu was 45.31 mg/kg with a corresponding (estimated) standard error of the mean of 5.26. It was also stated that the China background value for this concentration was 20. The results of various statistical tests described in the article were predicated on assuming normality.
a. Does the data provide strong evidence for concluding that the true average concentration in the sampled region exceeds the stated background value? Carry out a test at significance level .01. Does the result surprise you? Explain.
b. Referring back to the test of (a), how likely is it that the P-value would be at least .01 when the true average concentration is 50 and the true standard deviation of concentration is 10?