Question THREE[15]      Part A Do one of part A or part B ((Eager beavers: If you do both the best will be counted.))

Here are six samples from the tile population sampled in assignment six They are not random, each sample is chosen so that two are small and two are large. However, each sample is independent of other samples. sample # | sample data | TOTAL sample 1 | 35 35 160 140 | 370 sample 2 | 65 155 70 35 | 325 sample 3 | 50 75 95 60 | 280 sample 4 | 40 35 95 155 | 325 sample 5 | 40 100 100 40 | 280 sample 6 | 200 40 35 100 | 375 The average of all 24 observations is 81.46 The standard deviation of all 24 observations is 49.09 This question concerns the the precision of the average, 81.46 (i.e of the standard deviation, call it sigma, of the process that produced this average. (We investigated this sort of thing when looking for a possible bias in the judgement samples of tiles taken in assignment 6.) a) For random samples, 10.02 = 49.09/sqrt(24), is a valid estimate of sigma. Why is it not valid for the samples of this data?
   »»»»  Some of 24 items are not statistically independent of others. b) Calculate a valid estimate of sigma from the data
   »»»» The averages of the separate samples: 92.5 81.25 70 81.25 70 93.75
   »»»» The standard deviation of the above: 10.351
   »»»» Estimated sigma: 4.23 c) The population mean of the tile areas is 84.93. Does this data provide evidence that this sampling procedure is biased? Use (b) in answering this. Also explain, this item will be graded on the explanation.
   »»»» The sample average, 81.46 is within less than its precion,
   »»»» 4.23, of the population average, 84.93. There is no
   »»»» reason to reject the null hypothesis that the expectation of
   »»»» the sampling process is 84.93.