Chapter 9.1, Problem 14E

The level of monoamine oxidase (MAO) activity in blood platelets (nm/mg protein/h) was determined for each individual in a sample of 43 chronic schizophrenics, resulting in $\bar{X}$ = 2.69 and s₁ = 2.30, as well as for 45 normal subjects, resulting in $\bar{Y}$ = 6.35 and s₂ = 4.03. Does this data strongly suggest that true average MAO activity for normal subjects is more than twice the activity level for schizophrenics? Derive a test procedure and carry out the test using α = .01. [Hint: H₀ and H_a here have a different form from the three standard cases. Let μ₁ and μ₂ refer to true average MAO activity for schizophrenics and normal subjects, respectively, and consider the parameter θ =2μ₁ − μ₂. Write H₀ and H_a in terms of θ, estimate θ, and derive ${\hat{\sigma }}_{\hat{\theta }}$(“Reduced Monoamine Oxidase Activity in Blood Platelets from Schizophrenic Patients,” Nature, July 28, 1972: 225–226).]