# 生物統計研讀筆記 - Establish Hypothesis 建立假設

• ## Typical steps of making hypothesis

• State the problem
• Formulate the null and alternative hypotheses
• Null hypothesis 等號方向與情境描述方向相反，Greater than -> $\leq$
• Choose the level of significance
• the probability of rejecting a true null hypothesis
• Determine the appropriate test statistic $\alpha: level$
• Calculate the appropriate test statistic
• Determine the critical values for the sampling distribution and appropriate level of significance, (or Determine the $P :value$ of the test statistic)
• Compare the test statistic to the critical value
• Based on the comparison, accept or reject hypothesis
• $Z : value$ : c.v.’s = ±1.960, -1.960 < 1.8 < 1.960 -> Not extreme enough to reject null hypothesis
• $P :value$ : 0.0718 > 0.05, which is the level of signiﬁcance. -> Not rare enough to reject the null hypothesis
• Above are two-taills, *how are the left-tail and right tail conditions? *
• ## Type I and Type II error

• Type I error:
• When $H_0$ is really true, but we reject $H_0$ based on the statistic result
• P(Type I error) = the probability of rejecting a true null hypothesis.
• Type II error:
• When $H_0$ is really false, but we accept $H_0$ based on the statistic result
• P(Type II error) = the probability of accepting a false null hypothesis.