Chapter 9 Notes (4)

# Chapter 9 Notes (4) - A signiﬁcance test analyzes the...

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Unformatted text preview: A signiﬁcance test analyzes the strength of the evidence against the null hypothesis We start by presuming that H0 is true The burden of proof is on H The approach used in hypothesis testing is called a proof by contradiction To convince ourselves that H is true, we must show that data contradict H o VVVVVV I. Ifthe P—value is small, the data contradict H0 and support H m > A two-sided alternative hypothesis has the form H : p 1: p0 a > The P-value is the two-tail probability under the standard normal curve > We calculate this by ﬁnding the tail probability in a single tail and then doubling it it Analogy: Legal trial ' Null Hypothesis: Defendant is Innocent Alternative Hypothesis: Defendant is Guilty - If the jury acquits the defendant, this does not mean that it accepts the defendant's claim of innocence 0 Innocence is plausible, because guilt has not been established beyond a reasonable doubt > Step I: Assumptions 0 The variable is quantitative 0 The data are obtained using randomization 0 The population distribution is approximately normal. This is most crucial when n is small and H is one-sided. E > Step 2: Hypotheses: > The null hypothesis has the form: 0 H0: p = 1.10 > The alternative hypothesis has the form: 0 H : u > uo (one-sided test) or a 0 H : u < “o (one-sided test) or a ' H : u :;E p0 (two-sided test) Step 3: Test Statistic - The test statistic measures how far the sample mean falls from the null hypothesis value “0’ as measured by the number of standard errors between them - The test statistic is: t=x—‘u° ,where sear/J; f=x_ﬂ" se six/n ...
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