Marika wants to estimate how many coffees sold per week at the coffee shops and cafes in and around the University of Canterbury. She plans to do this by taking a sample of the coffee shops cafes and asking them how many coffees they have sold in the last week. There are 16 coffee shops and cafes (A to P).

1. Marika went to all the coffee shops and cafes first and counted how many chairs they have. Her results are given in the table below. She of course does not know the number of coffees sold.

Store	Number of seats	Number of coffees sold in week (yi)
A	8	455
B	24	3512
C	15	1129
D	58	6424
E	4	265
F	90	8530
G	31	3560
H	11	567
I	35	2633
J	5	699
K	14	756
L	52	8267
M	36	1742
N	160	13440
O	7	654
P	5	656

Using number of seats as an auxiliary variable, describe how Marika could take a random sample of the coffee shops and cafes with replacement with the probability of selection proportional to number of seats. Marika can use pencil and paper or has basic skills with a spreadsheet, but does not know R.

2. Choose 4 sample points using your method from (a) and estimate the total number of coffees sold during the week in all the coffee shops and cafes. That is, Marika has gone and got the measure in the third column.
3. What is the variance of your estimated total? Use the variance of your sample as the estimate of the variance of the population.