Introduction to Mathematical Statistics
Introduction to Mathematical Statistics STAT 312
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Mrs. Triston Collier
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This 1 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 312 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/205088/stat-312-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
Stat 312 Fall 2003 09252003 Discussion 4 Con dence Intervals A lOOl a con dence interval for the mean M of the normal population when the value of a is know is given y a a lti 2042 39 7i 2042 39 Choice of Sample Size The general formula for the sample size n necessary to ensure that the resulting 100la con dence interval has a width of w is obtained from w 2 2042 a n as Example Assume that the helium porosity in percentage of coal samples taken from any particular seam is normally distributed with true standard deviation 75 Compute a 95 Cl for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 485 3 0quot Compute a 98 Cl for true average porosity of another seam based on 16 specimens with a sample average porosity of 456 o How large a sample size is necessary if the width of the 95 interval is to be 40 d What sample size is necessary to estimate true average porosity to within 2 with 99 con dence A Large Sample Interval for M If n is suf cient large the largesample con dence interval for M with con dence level approximately lOOl a is i i 2042 A Con dence Interval for a Population Proportion A con dence interval for a population proportion p with con dence level approximately 100la is 2 AA 2 1324 i2w2v q l 222n OneSided Con dence Intervals A largesample upper con dence bound for M is S Mltizai and a largesample lower con dence bound for M is 7 s M gt z 7 2a W Example A random sample of 539 households from a certain midwestern city was selected and it was determined that 133 of these households owned at least one rearm The social determinants of Gun Ownership Self Protection in an Urban Environment77 Criminology 1997 629640 Using a 95 con dence level calculate a lower con dence bound for the proportion of all households in this city that own at least one rearm Example A random sample of 110 lightning ashes in a certain region resulted in a sample average radar echo duration of 81 sec and sample standard deviation of 34 sec Lightning Strikes to an Airplane in a Thunderstorm J of Aircraft 1984 607611 Calculate a 99 twosided con dence interval for the true average echo duration M TingLi Lin
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