3. (6.5) (6 -point problem) Interest is in testing whether a coin is "fair", that is, H0:p= 0.5 versus Ha
:p=0.5, where p is the probability that the coin toss is heads. The coin is tossed eight times. We
reject the null hypotheses if we get all heads or all tails. (a) What is the test size for this decision
rule? (Hint: this is to compute the P (Type I Error )=P( Reject H0H0 is true ) ) (b) Suppose the
alternative is true and, in particular, p=0.8. What is the power of the test? (Hint: this is to compute
1P (Type II Error) =P (reject H0Ha is true)).
3 65 6 point problem Interest is in testing whether a.pdf
1. 3. (6.5) (6 -point problem) Interest is in testing whether a coin is "fair", that is, H0:p= 0.5 versus Ha
:p=0.5, where p is the probability that the coin toss is heads. The coin is tossed eight times. We
reject the null hypotheses if we get all heads or all tails. (a) What is the test size for this decision
rule? (Hint: this is to compute the P (Type I Error )=P( Reject H0H0 is true ) ) (b) Suppose the
alternative is true and, in particular, p=0.8. What is the power of the test? (Hint: this is to compute
1P (Type II Error) =P (reject H0Ha is true))
