STA6126 Chapter 6 - Revised on 19:08 a11/p11 Chapter 6...

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Revised on 11/9/2011 19:08 a11/p11Chapter 6Statistical Inference: Significance TestsDefinition:A hypothesisis a statement (sentence) with a subject (a parameter), object (a number) and a verb (one of the following: =, ≠, <, >).Hypotheses come in pairs:The Null hypothesis (Ho): is a hypothesis of no change (status quo). It represents our current knowledge about the value of the parameter.Some examples of are Ho: μ = 5, or Ho: π = 0.4. The Alternative Hypothesis (Ha): is a statement of change (a claim, conjecture, guess) in the value of the parameter.Some examples are Ha: μ > 2or Ho: μ < 6 or Ha: μ ≠ 10More examplesHa: π ≠ 0.9, or Ha: π < 0.4 or Ha: π > 0.6Six Steps of Hypothesis Testing:1.Specify the assumptionsDefine the random variable (population)Define the distribution of the population Define the parameter of the distribution (known and unknown)Specify data collection method and type of dataSpecify the sample size.2.Specify the hypotheses: Equality is ALWAYS with Ho.Always in pairs (Ho and Ha)Ho is the hypothesis of the current knowledge (statusquo)Ha is the hypothesis of change.When one of the two hypotheses is true the other one MUST be false.3.Specify the test statistic: For testing hypotheses about the population mean,μ, the test statistic is always0(1)~/nXTtSnμ--=, where μ0is the value of μ specified by Ho.For testing hypotheses about the population proportion,π, the test statistic is always 000~(0,1)(1)pZNnπππ-=-STA6126 Chapter 5, Page 1 of 12
4.Calculate the p-value:
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)5.Make a decision:Either “reject Ho” or “Do not reject Ho.”Decision Rule is ALWAYSReject Ho if p-value ≤ α”6.Write a conclusion:Explain the decision in layman’s language with no technical jargon (except specifying the p-value or α).6.1Tests for Population Means1.Assumptions:a)SRSb)Quantitative variablec)Normal populationd)μ = mean of the population2.Hypotheses:Ho: μ = μ0, where μ0is a number; the value of μ specified by Ho.Ha: μ ≠ μ0or Ha: μ < μ0or Ha: μ > μ03.Test Statistic:0(1)~/nXTtSnμ--=. Remember that when the df is large, t approaches Z.4.P-ValueDepends on Ha:If Ha: μ < μ0then p-value = P(T ≤ Tcal)If Ha: μ > μ0then p-value = P(T ≥ Tcal)If Ha: μ ≠ μ0then p-value = 2 × P(T ≥ | Tcal| )STA6126 Chapter 5, Page 2 of 12

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