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Unformatted text preview: Cheat Sheet FTest: Test of population variance Chi^2 Test: ttest: When looking for a population mean given the sample deviation Ptest: Proportion test when there are 2 **First, find the rejection region, and then the test statistic Hypothesis Testing: Chi^2 Test & Probability of making an error! The hypotheses are 10 : 2 ≤ X H σ and 10 : 2 1 X H σ and are tested at the 5% significance level using a sample size of 21 to estimate the population variance. If the population variance 75045 . 32 2 = X σ , what is the probability of making a Type II error ? So, .05 with 20 degrees of freedom STEP 1: Rejection region : 4104 . 31 2 20 , 05 . 2 = ≥ χ χ ****Look at the chart**** 7052 . 15 20 4104 . 31 10 ) 1 ( ) 1 ( 2 2 2 2 2 2 2 = ⋅ = ⋅ = → = L s n s s n χ σ σ χ ***Change formula because you have chi^2 from above. Or TI89 STEP 2: FIND THR TEST RR: Rejection region: 7052 . 15 2 ≥ L s 025 . ) 59083 . 9 P( ) 32.75045 15.7052 20 ) 1 ( P( ) ( ) 32.75045 7052 . 15 ( ) ( ) 32.75045 ( ) true is H Null Rejecting Not ( ) ( 2 2 2 2 2 H 2 2 H 2 2 1 = < = ⋅ < ⋅ = = = < = = < = = χ σ χ σ σ s n II Type P s P II Type P s s P P II Type P L Hypothesis Testing – Ptest The hypotheses that 1 . : 2 1 ≥ p p H and 1 . : 2 1 1 < p p H are tested at the 1% significance level using a sample proportion from population 1 50 . ˆ 1 = p and a sample proportion from population 2 60 . ˆ 2 = p . Assume the distribution of the difference in the sample proportions ( 2 1 ˆ ˆ p p ) is normally distributed and the standard deviation of the difference of the sample proportion is 10 . 2 1 ˆ ˆ = p p σ . If 62 . 1 = p and 56 . 2 = p what happens in the problem? . 2 10 . 20 . 10 . 1 . ) 60 . 50 . ( ) ( ) ˆ ˆ ( ) ˆ ˆ ( 2 1 2 1 2 1 ˆ ˆ 2 1 2 1 ˆ ˆ ˆ ˆ 2 1 = = = = = p p p p p p p p p p p p Z σ σ μ Rejection Region: 33 . 2 01 . = ≤ z z ****GO TO THE P CHART!**** (.001 comes from sig.) If 62 . 1 = p and 56 . 2 = p then 10 . 06 . 56 . 62 . 2 1 < = = p p and the alternative is true. We do not reject the null when the alternative is true, we therefore have made a Type II Error . Hypothesis testing – FTEST The hypothesis that 2 2 2 1 10 : X X H σ σ ⋅ ≤ and 2 2 1 2 1 10 : X X H σ σ ⋅ is tested at the 5% significance level, where the sample variance of population 1 500 2 1 = X s is obtained from a sample of size 4 and the sample variance of population 2 10 2 2 = X s is obtained from a sample of size 6. If 400 2 1 = X σ and 50 2 2 = X σ which of the following statements is correct....
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This note was uploaded on 10/30/2008 for the course ECON 010 taught by Professor Giummo during the Spring '08 term at Dartmouth.
 Spring '08
 GIUMMO
 Economics

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