Lecture18 - lecture 18, Hypothesis Testing II 1/29 z Tests...

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Unformatted text preview: lecture 18, Hypothesis Testing II 1/29 z Tests about a Population Mean: σ Known Testing a “Less Than” Alternative Critical Value Rule The p-value Approach Testing a “Not Equal To” Alternative Critical Value Rule p-value Approach A brief summary The Effect of Sample Size t Tests about a Population Mean: σ Unknown Hypothesis Testing for a Population Proportion lecture 18, Hypothesis Testing II Outline 1 z Tests about a Population Mean: σ Known Testing a “Less Than” Alternative Critical Value Rule The p-value Approach Testing a “Not Equal To” Alternative Critical Value Rule p-value Approach A brief summary The Effect of Sample Size 2 t Tests about a Population Mean: σ Unknown 3 Hypothesis Testing for a Population Proportion lecture 18, Hypothesis Testing II 2/29 z Tests about a Population Mean: σ Known Testing a “Less Than” Alternative Critical Value Rule The p-value Approach Testing a “Not Equal To” Alternative Critical Value Rule p-value Approach A brief summary The Effect of Sample Size t Tests about a Population Mean: σ Unknown Hypothesis Testing for a Population Proportion lecture 18, Hypothesis Testing II z Tests about a Population Mean: σ Known Testing a “Less Than” Alternative Testing a “Less Than” Alternative: Payment Time Case • With old billing system, the mean bill payment time μ was close to but not less than 39 days • It is hoped that the new billing system will reduce the mean bill payment time by more than 50% • Assume that σ is known to equal 4.2 1. State the null and alternative hypothesis • H : μ ≥ 19 . 5 versus H a : μ < 19 . 5 • Effective null hypothesis H : μ = 19 . 5 ( versus H a : μ < 19 . 5 ) lecture 18, Hypothesis Testing II 3/29 z Tests about a Population Mean: σ Known Testing a “Less Than” Alternative Critical Value Rule The p-value Approach Testing a “Not Equal To” Alternative Critical Value Rule p-value Approach A brief summary The Effect of Sample Size t Tests about a Population Mean: σ Unknown Hypothesis Testing for a Population Proportion lecture 18, Hypothesis Testing II z Tests about a Population Mean: σ Known Testing a “Less Than” Alternative Testing a “Less Than” Alternative: Payment Time Case, ctd 2. Specify the significance level α • The firm require very strong evidence to conclude that μ is less than 19.5, set α = . 01 3. Select the test statistic: use the test statistic Z = ¯ X- μ σ/ √ n = ¯ X- 19 . 5 4 . 2 / √ n • Under the effective null hypothesis, Z has distribution. • A negative value of this test statistic results from a sample mean that is (greater/less ?) than 19.5 days, hence provides evidence (against/in favor of?) H (against/in favor of?) H a • A positive value? lecture 18, Hypothesis Testing II 4/29 z Tests about a Population Mean: σ Known Testing a “Less Than” Alternative Critical Value Rule The p-value Approach Testing a “Not Equal To” Alternative Critical Value Rule p-value Approach A brief summary...
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Lecture18 - lecture 18, Hypothesis Testing II 1/29 z Tests...

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