# Answer in Statistics and Probability for Anand #86832

A decision rule is a procedure that the researcher uses to decide whether to accept or reject the null hypothesis.

Two types of errors can result from a decision rule.

Type I error. A Type I error occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level, and is often denoted by α.

Type II error. A Type II error occurs when the researcher accepts a null hypothesis that is false. The probability of committing a Type II error is called Beta, and is often denoted by β. The probability of not committing a Type II error is called the Power of the test.

We have Binomial distribution for every coin

“P(X=x)=dbinom{n}{x}p^x(1-p)^{n-x}”

Null hypothesis is that coin is unbiased (head comes up at least twice). Alternative hypothesis is that coin is biased.

Level of significance is probability to reject true null hypothesis:

“alpha=dbinom{5}{0}({1over 2})^0(1-{1 over 2})^{5-0}+dbinom{5}{1}({1over 2})^1(1-{1 over 2})^{5-1}”

“alpha={1 over 32}+{5 over 32}={3 over 16}=0.1875”

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

“1-beta=dbinom{5}{0}({2over 5})^0(1-{2 over 5})^{5-0}+dbinom{5}{1}({2over 5})^1(1-{2 over 5})^{5-1}”

“1-beta={243 over 3125}+{810 over 3125}={1053 over 3125}=0.33696”

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