AEM 201 1st Edition Lecture 19PREVIOUS LECTUREI. Interval EstimationII. Interval Estimation of the Population Mean-Population Standard Deviation KnownIII. Interval Estimation of the Population Mean-Population Standard Deviation UnknownCURRENT LECTUREI. Interval Estimation of the Population Mean-Population Standard Deviation UnknownII. Interval Estimation of the Population ProportionINTERVAL ESTIMATION OF THE POPULATION MEAN-POPULATIONSTANDARD DEVIATION UNKNOWN- Degrees of freedom=(n-1)- A t distribution becomes a z distribution as it approaches infinity-it becomes more normal- We must know the degrees of freedom and a/2 in order to use the t-tables- We can assume a distribution is normal if we are told it is normal- Confidence levels using t-tables are wider than confidence intervals derived using the standard normal table- The more observations we have, the surer we are about our results-Therefore, smaller and narrower intervals- We can use summary data to find confidence intervals- Note that it can be shown that the sample standard deviation is an extremely reliable estimator of the parent population’s standard deviation if we take a sufficiently large sample (n is greater than or equal to 30)- IF we know the population standard deviation and state the desired margin of error (denoted as E). The sample size is necessary to ensure a desired confidence level and margin of errorThese 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.- This is nothing but an algebraic manipulation of the definition of the margin of errorINTERVAL ESTIMATION OF THE POPULATION PROPORTION- Recall that if the sample size is sufficiently large (np is greater than equal to 5) and n(1-p is greater than or equal to 5) that p bar is approximately normally distributed with a mean of p andstandard deviation of:- You can sub p bar in for p.- Another alternative is to sub in .5 for pConservative and safe because it makes the marginal
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