Answer in Statistics and Probability for Anand #86943

Null hypothesis is that coin is unbiased. Alternative hypothesis is that coin is biased.

Level of significance is probability to reject true null hypothesis:

“alpha=P_0(less than two heads)=P_0(0 heads)+P_0(1 heads)=”“=dbinom{5}{0}({1 over 2})^0(1-{1 over 2})^{5-0}+dbinom{5}{1}({1 over 2})^1(1-{1 over 2})^{5-1}=”“{3 over 16}=0.1875”

Power of the test is the probability to reject null hypothesis while alternative is true:

“alpha=P(less than two heads)=P(0 heads)+P(1 heads)=”“=dbinom{5}{0}({2 over 5})^0(1-{2 over 5})^{5-0}+dbinom{5}{1}({2 over 5})^1(1-{2 over 5})^{5-1}=”“={1053 over 3125}=0.33696”