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MSci_609_Inference_using_Hypothesis_test

# MSci_609_Inference_using_Hypothesis_test - TESTS OF...

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2/5/2011 1 T E S T S O F H Y P O T H E S I S 1 / 2 I N S T R U C T O R : A M E R O B E I D I Statistical Methods 2 E ti ti Hypothesis Inferential Statistics Descriptive Statistics Estimation Testing Interval Estimation Point Estimation

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2/5/2011 2 A belief about a population I believe the mean GPA of this 3 parameter Parameter is population mean, proportion, variance, or any statistic Must be stated before analysis class is 3.8! . I believe the population mean age is 50 (hypothesis). Reject hypothesis! Not 4 Population close. Mean X = 20 Random sample
2/5/2011 3 In any hypothesis testing there are two hypotheses (exactly one of which must be true). N ll h th i H th t t i t j t d til 5 1. Null hypothesis o , the status quo, is not rejected until proven incorrect. Equality is always part of H 0 (e.g. “=” , “ ” , “ ”). 2. Alternate hypothesis H a , represents what we wish to prove or establish. “<” and “>” always part of H 1 The aim of the hypothesis test, is to determine whether in fact H o can be falsified , and consequently that H a b d can be accepted. Hence, the null hypothesis is the statement being tested, and we need specific value to include in our calculations. We turn to H a only if the data suggests that H 0 is false. 1. Is what we test 2 Has serious outcome if incorrect decision made 6 2. 3. Most often has equality sign in the relationship operator: , , or 4. Designated H 0 (pronounced H-oh) 5. Specified as H 0 : population parameter some i l numeric value Specified with = sign even if or

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2/5/2011 4 1. Opposite of null hypothesis 2 Has inequality sign:   or 7 2. , , or 3. Designated H a 4. Specified H a :   , , or some value Example problem: Test that the population mean is not 3 8 Steps: State the question statistically (   3) State the opposite statistically ( = 3) Notice here that both are mutually exclusive Select the alternative hypothesis (   3) Has the , < , or > sign State the null hypothesis ( = 3)
2/5/2011 5 Example problem: Is the population average amount of TV viewing 12 hours? 9 State the question statistically: = 12 State the opposite statistically:   12 Select the alternative hypothesis: H a :   12 State the null hypothesis: H 0 : = 12 Example problem: Is the population average amount of TV viewing different from 12 hours? 10 State the question statistically:   12 State the opposite statistically: = 12 Select the alternative hypothesis: H a :   12 State the null hypothesis: H 0 : = 12

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2/5/2011 6 Example problem: Is the average cost per hat less than or equal to \$20? 11 State the question statistically:   20 State the opposite statistically:   20 Select the alternative hypothesis: H a :   20 State the null hypothesis: H 0 :   20 Example problem: Is the average amount spent in the bookstore greater than \$25?
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