# Find the required sample size to force the # margin of error to be at a desired level. # # This applies to cases where we know the # population standard deviation. (Although, # if you have at least a rough guess of that, # perhaps by looking at the standard deviation # of samples from some earlier work then you could # adapt this methodology as an approximation even # if you did not know the standard deviation of # the population.) # So, here is a problem. We know that the # standard deviation in the population is 5.36. # we want to generate a 97% confidence interval # for the population mean. What sample size # would we need to get the margin of error down # to 1.5 or lower? # We know that the margin of error is # MOE =z_alpha_over_2*pop_sigma/sqrt( samp_size) # and if we solve that equation for samp_size # we get # samp_size = (z_alpha_over_2*pop_sigma/MOE)^2 # # but for our problem, we know all of the # values on the right z_alpha_over_2 <- qnorm( (1-0.97)/2) z_alpha_over_2 # # so samp_size <- (z_alpha_over_2*5.36/1.5)^2 samp_size # but since you can not get fractional # sample sizes we round up so that the MOE # is the desired 1.5 or less. # our sample size would be 61. # # Of course we could have used the provided # function, find_samp_size() source( "../findsampsize.R") # note missing _'s find_samp_size( 5.36, 0.97, 1.5)