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# Weekly Notes Eight TMATH 110 C

University of Washington Tacoma

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This 2 page Class Notes was uploaded by Qihua Wu on Sunday November 22, 2015. The Class Notes belongs to TMATH 110 C at University of Washington Tacoma taught by KENNEDY,MAUREEN C. in Fall 2015. Since its upload, it has received 22 views. For similar materials see Intro Stat Applications in Math at University of Washington Tacoma.

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Date Created: 11/22/15

Interval Estimates Recall that point estimators are the best approximations of the population parameter however since they only give single values for population parameter they still contain errors due to sampling variability it is unlikely to have the exact value of the population parameter from estimators Therefore We calculate the range of values for the population parameter so we can be more con dent that the exact value of the population parameter is what we had estimated We do so by using the data from a single sample Remember we only use estimation when the population parameters are unknown Con dence intervals We use this to characterize how much we are sure the population parameter is within our estimated range 100 is the con dence level whereas oz is the signi cance level signi cance level means how likely the population parameter is outside of our range 1 oz100 is the con dence interval lts lower boundary is the sample mean margin of error and upper boundary is the sample mean margin of error with population mean in between the lower and upper boundaries Width of con dence interval is determined by con dence level variability and sample size as con dence level or variability increase the con dence interval range increases as sample size increases the width of the interval decreases Normal times the only thing we can control is the sample size so to reduce the interval width the only thing we can to is to increase the sample size Sampling Error For point estimate the sampling error is the distance between the sample mean and the population mean we nd it by using sample mean population mean Margin of Error E Margin of error is the maximum distance above or below the population mean that contains 1cx100 of the sample means If cx1 then the margins of error is the maximum distance abovebelow the population mean that contains 90 of the sample mean It is the absolute value of the distance Don t forget the units since it is the difference between the two means the unit is the same as the mean Recall that 2 sample meanpopulation mean standard deviation of sample mean sample population sizequot5 and E absolute value of sample mean population mean We get Za2 E standard deviation of sample mean sample population sizequot5 Where Z M is the critical 2 score since cx2 is the probability at each tail of the distribution Some useful 2 values to remember for level of con dence 90 con dence is 1645 95 con dence is 196 99 con dence is 2575 When we input sample data to calculate our con dence level the probability 1oz is no longer valid since the random process is being realized so either the population parameter is within the interval or not but we can say instead how much con dence we are sure the population would be within the interval If given the width of the con dence interval margin of error is half of the width since the width is 2E the upper boundary is plus E and the lower boundary is minus E

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