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We have a random sample of n from the population. We can find the mean and standard deviation of the proportion of that sample that has the characteristic. X 1, X2, ..., Xn are n random variables that are independent and identically distributed with mean ? And standard deviation ?. Sn= X1+X2+...+Xn is the sample sum. We can show E (Sn)=n? And SD (Sn)=?
n. CLT states: Sn-n?
/0,1: as n
Question 3
Point estimates summarize the sample by a single number that is an estimate of the population parameter. An interval estimate is a range of values within which the true parameter lies with higher probability. In any estimation problem, we need to obtain both a point estimate and an interval estimate. The point estimate is our best guess of the true value of the parameter, while the interval estimate gives a measure of accuracy of that point estimate by providing an interval that contains plausible values.
To construct a confidence interval for a single unknown population mean ?, where the population standard deviation is known, we need x-as an estimate for ? And we need the margin of error. The margin of error is called the error bound for a population mean (EBM). The sample mean x? is the point estimate of the unknown population mean ?. The confidence interval estimate will have the form:(point estimate - error bound, point estimate + error bound) or, in symbols,(x?
EBM, x?+EBM) the margin of error depends...
The confidence level is often considered the probability that the calculated confidence interval estimate will contain the true population parameter. However, it is more accurate to state that the confidence level is the percent of confidence intervals that contain the true population parameter when repeated samples are taken. Most often, it is the choice of the person constructing the confidence interval to choose a confidence level of 90% or higher because that person wants to be reasonably certain of his or her conclusions.
Suppose we have collected data from a sample. We know the sample mean but we do not know the mean for the entire population. The sample mean is 7 and the error bound for the mean is 2.5.x?= 7 and EBM=2.5. The confidence interval is (7-2.5,7+2.5); calculating the values gives
(4.5,9.5).If the confidence level (CL) is 95%, then we say that we estimate with 95% confidence that the true value of the population mean is between 4.5 and 9.5.
References
Frerichs, R. (2008). Rapid Surveys. Simple Random Sampling. Retrieved from http://www.ph.ucla.edu/epi/rapidsurveys/RScourse/RSbook_ch3.pdf
McClave, J. Benson, G. & Sinchich, T. (2011). Statistics for Business and Economics 11th edition. 2011 Pearson Education.
"Normal Distribution." Wolfram Math World. Viewed 8 May 2013. Retrieved from http://mathworld.wolfram.com/NormalDistribution.html
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