{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MODULE 5 THE WHOLE MODULE

MODULE 5 THE WHOLE MODULE - 5 Hypothesis Testing Dave...

This preview shows pages 1–8. Sign up to view the full content.

5. Hypothesis Testing Dave Goldsman Georgia Institute of Technology, Atlanta, GA, USA 8/21/10 Goldsman 8/21/10 1 / 64

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Outline 1 Introduction to Hypothesis Testing 2 Normal Mean Tests (variance known) Simple Hypothesis Test Test Design Two-Sample Normal Mean Tests 3 Normal Mean Tests (variance unknown) Simple Hypothesis Test Two-Sample Normal Mean Tests Pooled t -Test Approximate t -Test Paired t -Test 4 Other Hypothesis Tests Normal Variance Test Two-Sample Test for Equal Variances Bernoulli Proportion Test Goldsman 8/21/10 2 / 64
Introduction to Hypothesis Testing Introduction to Hypothesis Testing General Approach 1. State a hypothesis. 2. Select a test statistic (to test whether or not the hypothesis is true). 3. Evaluate (calculate) the test statistic. 4. Interpret results — does the test statistic allow you to reject your hypothesis? Details follow. . . Goldsman 8/21/10 3 / 64

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Introduction to Hypothesis Testing 1. Hypotheses are simply statements or claims about parameter values. You perform a hypothesis test to prove or disprove the claim. Set up a null hypothesis ( H 0 ) and an alternative hypothesis ( H 1 ) to cover the entire parameter space. The null hyp sort of represents the “status quo”. Example: We claim that the mean weight of a filled package of chicken is μ 0 ounces. (We specify μ 0 .) H 0 : μ = μ 0 H 1 : μ negationslash = μ 0 This is a two-sided test . We’ll reject the claim if ˆ μ (an estimator of μ ) is “too high” or “too small”. Goldsman 8/21/10 4 / 64
Introduction to Hypothesis Testing Example: We claim that a certain brand of tires lasts for at least a mean of μ 0 miles. (We specify μ 0 .) H 0 : μ μ 0 H 1 : μ < μ 0 This is a one-sided test . We’ll reject the claim if ˆ μ is “too small”. Example: We claim that emissions from a certain type of car do not exceed a mean of μ 0 ppm. (We specify μ 0 .) H 0 : μ μ 0 H 1 : μ > μ 0 This is a one-sided test . We’ll reject the claim if ˆ μ is “too large”. Goldsman 8/21/10 5 / 64

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Introduction to Hypothesis Testing Idea: H 0 is the old, conservative “status quo”. H 1 is the new, radical hypothesis. Although you may not be toooo sure about the truth of H 0 , you won’t reject it in favor of H 1 unless you see substantial evidence in support of H 1 . “Innocent until proven guilty.” If you get substantial evidence supporting H 1 , you’ll decide to reject H 0 . Otherwise, you “fail to reject” H 0 . (This roughly means that you grudgingly accept H 0 .) Goldsman 8/21/10 6 / 64
Introduction to Hypothesis Testing 2. Select a test statistic (to test if H 0 is true). For instance, we could compare an estimator ˆ μ with μ 0 . The comparison is accomplished using a known sampling distribution (aka “test statistic”), e.g., z obs = ¯ X μ 0 σ/ n (if σ 2 is known) or t obs = ¯ X μ 0 S/ n (if σ 2 is unknown) Lots more details later.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}