Question

Please make sure to display your thought process? It is imperative to be able to follow how the answer was deduced. Please be as thorough as possible. Please address all parts of this question.

Consider a hypothesis test for the population mean value.

A) Explain the concept of type I and type II errors, with error probabilities denoted by a and b.

B) How do we decide whether to use one-sided or two-sided hypothesis tests? Give an example for both cases.

C) Explain briefly the concept of operating characteristic curves, in the context of this hypothesis test.

D) What is the effect of an increase in sample size on β, provided that a and the stated difference from H₀ are held constant?

E) If the null hypothesis is false, then how does β change as the difference between the true mean value and the hypothesized value increases?

Answer 1