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Lect20_L6_L7_handout

# Lect20_L6_L7_handout - lecture 20 Hypothesis Testing II...

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lecture 20, Hypothesis Testing II z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach Testing a “Less Than” Alternative Critical Value Rule The p -value Approach Summary of Testing a One-Sided Alternative lecture 20, Hypothesis Testing II Outline 1 z Tests about a Population Mean: σ Known 2 Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach 3 Testing a “Less Than” Alternative Critical Value Rule The p -value Approach 4 Summary of Testing a One-Sided Alternative

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lecture 20, Hypothesis Testing II z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach Testing a “Less Than” Alternative Critical Value Rule The p -value Approach Summary of Testing a One-Sided Alternative lecture 20, Hypothesis Testing II z Tests about a Population Mean: σ Known z Tests about a Population Mean: σ Known Test hypotheses about a population mean using the normal distribution: Called z tests Require that the population standard deviation σ is known In most real-world situations, σ is not known — But often is estimated from s of a single sample — When σ is unknown, test hypotheses about a population mean using the t distribution —to be talked about later Here, assume that we know σ Two approaches: (i) Critical Value Rule (sometimes also called Rejection Point Rule) (ii) p -value
lecture 20, Hypothesis Testing II z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach Testing a “Less Than” Alternative Critical Value Rule The p -value Approach Summary of Testing a One-Sided Alternative lecture 20, Hypothesis Testing II Testing a “Greater Than” Alternative Critical Value Rule Steps to Apply the Critical Value Rule 1 State the null and alternative hypotheses 2 Specify the significance level α 3 Select a test statistic 4 Determine the critical value rule for deciding whether or not to reject H 0 . Use the specified α to find the critical value 5 Collect the sample data and calculate the value of the test statistic 6 Decide whether to reject H 0 by using the test statistic and the critical value rule 7 Interpret the statistical results in real-world terms and assess their practical importance

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lecture 20, Hypothesis Testing II z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach Testing a “Less Than” Alternative Critical Value Rule The p -value Approach Summary of Testing a One-Sided Alternative lecture 20, Hypothesis Testing II Testing a “Greater Than” Alternative Critical Value Rule Testing a “Greater Than” Alternative: Trash Bag Case Tests show the trash bag has a mean breaking strength μ close to but not exceeding 50 lbs The new bag’s mean breaking strength is not known and is in question, but it is hoped it is stronger than the current one Assume that σ = 1 . 65
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Lect20_L6_L7_handout - lecture 20 Hypothesis Testing II...

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