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# ANSWERS PROBLEM SET 3.doc

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York University

Biology

BIOL 2060

Joel Shore

Fall

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PROBLEM SET 31 With a few words and diagrams define the standard deviation and standard error of the mean What is the purpose of using one versus the other The standard deviation is a descriptive statistic estimating the amount of variation in a populationThat is its use The standard error of the mean is used to provide information on how precisely the mean has been estimated The standard error of the mean can be interpreted asa the standard deviation of the sampling distribution of means of fixed size n from a population or more commonlyb it is a measure of precision of the estimate of a meanwhere the standard error of the mean is estimate by the standard deviation divided by the square root of the sample size draw distribution of population and sampling distribution of means to illustrate2 For each of the following data sets estimate the mean and the standard error of the mean do this by hand using SAS data set 1data set 2data set 3 data set 4114139816132316320221106195316100818481410010265921100Data twoinput d1d4cards114139816132316320221106195316100818481410010265921100proc means mean n std stderrrunThe SAS SystemThe MEANS Procedure VariableMeanNStd DevStd Errord15600000053646916516309506d218960000054694464820994285d347200000052023977396905150209d48644000053096271441384694683 Here are weights of fish kg sampled randomly from Lake St George 142 263 321 111 063 520Estimate the standard error the mean and the approximate 95 confidence limits for these dataTo obtain approximate 95 confidence limits first estimate the standard error of the meanData threeinput fishwt cards142 263 321 111 063 520proc means mean n std stderrrunThe SAS SystemThe MEANS Procedure MeanNStd DevStd Error2366666761691137706904041The approximate upper and lower limits are obtained asthe mean2standard error of meanso lower limit is 23672x06900986 upper limit is 23672x06903747so we are 95 confident that the true mean lies somewherebetween these upper and lower limits4 The following questions apply to probabilities of rolling various numbers using fair dicea What is the probability of rolling a single die andobtaining a 2 or a 6given these are mutually exclusive events Pr2 or 6Pr2Pr6161613b What is the probability of rolling a single die andobtaining a 2 and 6given these are mutually exclusive events it is impossible to get both of these so Pr2 and 60c What is the probability of rolling a die and obtaining a

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