```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.
```