Question

1. A statistician formulated a hypothesis test, specifying the value of α, the hypotheses H₀ and H_a, and the data-collection and analysis procedures to be used. Choose one of the following and write one or two sentences justifying your choice:

                        α + β < 1

                        α + β = 1

                        α + β > 1

                        Any of the above might be true – more information about this hypothesis test would be needed.

Answer 1

Suppose, for a test

• Random variable be
• Null hypothesis is
• Alternative hypothesis is
• Critical region is

Then,

Though these are probabilities over two complement regions, these are calculated over different parameters (as described in and respectively). Thus values of and can not be linked directly.

Hence, any one relation of

• 
• 
• 

can be true. More information about this hypothesis test is required to draw exact conclusion.