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Problems of estımatıon, POINT ESTIMATION, INTERVAL ESTIMATION , Confidence Interval for Population Mean ; explanation , question and solution
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INTERVAL ESTIMATION
INTERVAL ESTIMATION An interval estimation of an unknown population parameter θ can be demonstrated as follows: L ≤ θ ≤ U where L and U are the lower and upper limits, respectively. A natural question to ask at this stage is that how can we measure the correctness of the interval for this unknown population parameter? We may rephrase the question as “how much do you trust your interval to include real arithmetic mean of the population?” Therefore, we need the probability theory to support our decision about a correct interval estimate of the unknown population parameter is obtained.
CONFIDENCE INTERVAL FOR POPULATION MEAN There are two important situations in the calculation of confidence interval for a population mean. We will discuss these two situations now in detail. The first case is that we use sample data to estimate the unknown value of population mean μ with the value of sample mean x found from a random sample of size n , and also the population standard deviation σ is known beforehand. The second case is that we use sample data to estimate the unknown value of population μ with the value of sample mean x found from a random sample of size n , and also the population standard deviation σ is not known. In the second case, instead of the population standard deviation σ , the sample standard deviation s is used as the substitute.