3. Stratified sampling 6 MARKS The table below shows the population sizes for each of New Zealand's 16 regions, as at the 2018 Census. Region Population Northland 179,076 Auckland 1,571,718 Waikato 458,202 Bay of Plenty 308,499 Gisborne 47,517 Hawke's Bay 166,368 Taranaki 117,561 Manawatu-Wanganui 238,797 Wellington 506,814 West Coast 31,575 Canterbury 599,694 Otago 225,186 Southland 97,467 Tasman 52,389 Nelson 50,880 Marlborough 47,340 Suppose a survey sampled 1000 people from each region. (a) Calculate the sampling fractions for Auckland and West Coast to five decimal places. (2 MARKS) (b) What weight should Auckland and West Coast be given in analyses (one decimal place)? (2 MARKS) (c) What is the total sample size? (1 MARK) (d) What is the sum of weights across all people in the sample? (1 MARK)