Determining Sample Sizes For Estimating 

Situation We want to estimate the average life of certain batteries –We know it costs about $15 to test each battery –We want to be able to make a statement about average battery life that gives an interval that is “not too big” Do we need to set aside $500 to do this study? $2000? $10,000? $250,000?

Must Determine the Appropriate Sample Size, n The answer to the question depends on the following factors which we must first predetermine: –How wide an interval we are willing to accept (±E) –How likely the interval is to contain  (Confidence 1-  ) Recall the confidence interval is: This “±” part is E Irrelevant for the calculation Since we know z  /2, , and B, this means we have 1 equation in 1 unknown (n)

Example How large a sample must be taken to estimate the true mean of battery time to within  10 hours (with 95% confidence, given that  = 40)? 1.96(40/ ) = /10 = = 7.84 n = (7.84) 2 = ROUND UP = 62

Overall Cost So what is the overall cost of the study? –We will test 62 batteries –It costs $15 to test each battery $15(62) = $930Thus cost of study is $15(62) = $930

REVIEW To determine sample size, given , , and a bound for the “±” part = E round UPSolve and round UP To solve for the overall cost, if the cost per sample = c, TOTAL COST = c n