For a cooking oil company, the price they are paid for coconuts in large shipments is based on the amount of coconut extract from the load.  Therefore, there is a need to determine the amount of coconut extract in the whole load prior to extraction.  A sample of n coconut can be taken and find y1, . . . , yn , the amount of coconut extract in these coconuts.    Ny is hard to get in this case because N is hard to count.  How can the total amount of coconut extract from a load shipment be measured?  Using the total weight would be a good idea and easy to obtain.  The relationship between the weight of the load and the weight of the coconut extract one obtains can be used.  As it turns out, 15 coconuts selected by simple random sampling were weighed and also extracted.  The total weight of the coconut shipment was found to be 900 kg

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For a cooking oil company, the price they are paid for coconuts in large shipments is based on the amount of coconut extract from the load.  Therefore, there is a need to determine the amount of coconut extract in the whole load prior to extraction.  A sample of n coconut can be taken and find y1, . . . , yn , the amount of coconut extract in these coconuts.

  
Ny is hard to get in this case because N is hard to count.  How can the total amount of coconut extract from a load shipment be measured?  Using the total weight would be a good idea and easy to obtain.  The relationship between the weight of the load and the weight of the coconut extract one obtains can be used.  As it turns out, 15 coconuts selected by simple random sampling were weighed and also extracted.  The total weight of the coconut shipment was found to be 900 kg.  Given these results (below):

look at the table (pic)

Question: 

  1. Suppose there were 6870 coconuts in the shipment.  Compute the variance of the regular SRS estimate of the total weight of the coconut extract for this shipment.
Weight of the coconut
extract in grams
Sampled coconut
Weight of the coconut in
grams
73
100
2
68
118
3
91
141
4
114
168
5
73
127
6.
123
173
7
127
182
8
73
96
50
82
10
73
132
11
77
118
12
109
146
13
96
150
14
50
73
15
100
159
Transcribed Image Text:Weight of the coconut extract in grams Sampled coconut Weight of the coconut in grams 73 100 2 68 118 3 91 141 4 114 168 5 73 127 6. 123 173 7 127 182 8 73 96 50 82 10 73 132 11 77 118 12 109 146 13 96 150 14 50 73 15 100 159
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