67. A new method for measuring phosphorus levels in soil is described in the article “A Rapid Method to Determine Total Phosphorus in Soils” (Soil Sci. Amer. J., 1988: 1301–1304).

Suppose a sample of 11 soil specimens, each with a true phosphorus content of 548 mg/kg, is analyzed using the new method. The resulting sample mean and standard deviation for phosphorus level are 587 and 10, respectively.

a. Is there evidence that the mean phosphorus level reported by the new method differs significantly from the true value of 548 mg/kg? Use 
.05.

b. What assumptions must you make for the test in part (a)

to be appropriate?