Math 130 Day 18 summary.pdf

Math 130 Day 18 summary.pdf - Sec 10.4 Hypothesis Tests for...

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Sec. 10.4: Hypothesis Tests for a Population Standard Deviation (or a Population Variance ) 𝜎 𝜎 2
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Idea Behind Hypothesis Tests (for ) To settle the dispute… 1. Take a sample (only one) 2. Calculate s If s = 10 , believe the king If s > 10 , believe the king If s < 10 , it depends! If s < 10 but close to 10, still believe the king If s < 10 but far from 10, then believe the peasant 𝜎
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Hypothesis Tests for (or ) Formulas and Info Quantity you are performing a hypothesis test for: (or ) 𝜒 2 = (𝑛 − 1)? 2 𝜎 2 Condition: Population from which samples are drawn have a NORMAL distribution Probability distribution: - distribution Test statistic formula: Significance level: 𝑑𝑓 = 𝑛 − 1 Degrees of freedom: (helps you determine the cutoff of the rejection region) 𝜎 𝜎 𝜒 2 𝜎 2 𝜎 2
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Calculating P Values (for 1 population or problems) For a left-tailed test The P-value is i.e. the P-value is the area to the left of the test statistic 𝜎 𝜎 2 𝑃(𝜒 2 < ?. ?. )
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Calculating P Values (for 1 population or problems)
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