AEM 201 1st Edition Lecture 17PREVIOUS LECTUREI. Desirable Characteristics of Point EstimatorsII. Sampling DistributionsIII. The Sampling Distribution of the Sample MeanCURRENT LECTUREI. The Sampling Distribution of the Sample MeanII. The Sampling Distribution of the Sample ProportionTHE SAMPLING DISTRIBUTION OF THE SAMPLE MEAN- Tolerance Interval: a range of values of a random variable that contains a specified proportion of a population. There are often derived so they are symmetric with the center of the variables probability distributiono If x bar is normally distributed, these two values will be equal- The proportion of population elements not included in the tolerance interval to be o The area between and the lower limit of the tolerance is 0.5- /2 o The area between and the upper limit of the tolerance is 0.5- /2- Since normally distributed, we can use the standard normal distribution tables to find the values of the standard normal variable z that produces such an interval (-z /2 and + z /2)- We will use the inverse standard normal function- We have been using tables to find the cumulative area under the standard normal curve for the given value of z-how we wish to find the value of z that results in a given cumulative area under the standard normal curve- Value of 1- for a tolerance interval is referred to as the ‘tolerance level’THE SAMPLING DISTRIBUTION OF THE SAMPLE PROPORTION- The Sampling Distribution of the Sample Proportion: the probability of a distribution associated with all possible values of the sample proportiono The expected value of this distribution is equal to the population proportionThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o The standard deviation (standard error) is computed below. Only if the population is infinite in a statistical sense (n/N is less than or equal to 0.05)- Central Limit Theorem (Proportion): when selecting a simple random sample from a population the sample distribution of p bar can be approximated by a normal probabilitydistribution as the sample size become large. Here we will consider n to be sufficient to assure that the Central Limit Theorem will force the potential values of p bar to be normally distributed if:o np is greater than or equal to and o n(1-p) is greater than or equal to 5- Larger the sample size the more accurate- We can also build a 1-a for a tolerance interval for p:- The Finite Population Correction Factor (fpcf): if the sample size n is large relative to the size of the population N (n is at least 5% of N) the standard error must be adjusted downward this is accomplished through multiplying the standard error by the
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