Question

1. Let p-: P(head) when a coin is tossed, and consider the hypotheses Ho : p-0.5 and H. : p-0.1. Suppose the coin is tossed 10 times, and te critcal region is defined by "get 2 heads or less". That is the null hypothesis is rejected if the number of observed heads is 2 or less. (a) Find the significance level of the test (a). (b) Find the power of the test (1 -B).

Answer 1

a)P(significance level) =P(getting 2 or less heads given p=0.5)=P(X<=2)=P(X=0)+P(X=1)+P(X=2)

=¹⁰C₀(0.5)⁰(0.5)¹⁰+¹⁰C₁(0.5)¹(0.5)⁹+¹⁰C₂(0.5)²(0.5)⁸=0.0547

b)

P(power of the test ) =P(getting 2 or less heads given p=0.1)=P(X<=2)=P(X=0)+P(X=1)+P(X=2)

=¹⁰C₀(0.1)⁰(0.9)¹⁰+¹⁰C₁(0.1)¹(0.9)⁹+¹⁰C₂(0.1)²(0.9)⁸=0.9298