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This 2 page Class Notes was uploaded by Uriah MacGyver on Saturday September 19, 2015. The Class Notes belongs to STAT200 at University of Delaware taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/207187/stat200-university-of-delaware in Statistics at University of Delaware.
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Date Created: 09/19/15
STAT 200 Review Sheet FACTORS INFLUENCING CONFIDENCE INTERVALS Confidence Interval for the Mean s x izm2 E ii telMAM J S Confidence Interval for a Pro ortion q P p i 2052 WHEN FACTOR FACTOR FACTOR GETS SMALLER REASON EXAMPLE n sample size C gets larger Smaller sample size means a larger 25150 354 standard error and less certainty 25500 112 a Type I error C gets larger If you accept smaller Type I error Z mm 196 ie the probability that a CI will not contain the mean you have to allow Z mm 2575 for a larger CI to be that sure La C C get smaller A smaller C means you are 95 CI uses ZDEZ 196 willing to accept more Type I error so we can have a tighter CI 99 CI uses Z Em 2575 O or 5 Std Dev of CI gets smaller If the population has less variability 25150 354 Popuatiom Std the sampling distribution will also Dev of sample have less variability 5f50 71 FACTORS INFLUENCING A HYPOTHESIS TEST 7c 0 7C 0 Test Statistic for a Mean Test Statistic for a Proportion Note PO comes from the Null Hypothesis WH EN FACTOR FACTOR FACTOR GETS SMALLER REASON EXAMPLE n Sample Size Test Statistic gets Smaller sample size means larger 25150 354 smaller standard error Tthe denominator o the test statistic will be larger and 253N500 112 2 or t will be smaller a Type I error Test Statistic unchanged The rejection region gets larger Z mm 196 Rejection region 2 gets making it more difficult to reject HE larger Z mm 2575 One or 2 Nature of Test Statistic unchanged With a onetailed test all of or is put TwoTailed Z mm 196 Taned Aternative Rejection region 2 gets into the one a39l Test Hypothesis smallerwith 1tailed test One Tailed Zn5 1645 O or 5 Std Dev of Test Statistic gets larger If the population has less variability 25150 354 Popuatiom std the sampling distribution has less variability and denominator of the 5f50 71 Dev of sample TS is smaller DIFFERENCE OF MEANS FORMULAS Standard Error estimate for Large Sample Difference of Means Confidence Interval for Large Sample Difference of Means Test Statistic for Large Sample Difference of Means Note DO comes from the Null Hypothesis Standard Error estimate for Small Sample Difference of Means Assumes Independent random samples approximate normal distribution 01 02 so we pool our estimate S2 quot1 1S12 quotz 1SzZ mm2 639 2 1 1 S Xer 17 n1 n2 Confidence Interval for Small Sample Difference of Means f1 f2 i tom n1n272df are equa hypothesis we assume that p1 p2 of successes for each sample If we have a null hypothesis where the two proportions I We pool the estimate of pp because under the null Pool estimate of p where X1 and x2 are the number Test Statistic for Small Sample 7c1 f2 DO Difference of Means t 1 1 s2 Note DO comes from the Null Hypothesis quot1 quotz DFFERENCEOFPROPORHONSFORMULAS Standard Error estimate for Large Sample x x Difference of Proportions for Hypothesis Test 2 P quot1 quot2 A 1 1 OPrpz I7qu n 1n 2 Test Statistic for Large Sample Difference of Proportions Note DO comes from the Null Hypothesis P1 p2Do Pqii 171771 n2 2 Confidence Interval for Large Sample Difference of Proportions P1q1 quz i V P1 P2 2052 n1 n2
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