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(1) Suppose you want to design a poll to predict the outcome of the presidentialelections. Explain how you would sample the population for the poll. Saywhat type of sample would you use and explain specically how you woulddesign such a sample. Explain why such a sample is the appropriate onefor this situation.(2) After describing your honest poll explain how a dishonest pollster can designa poll that might look fair but is likely to produce a result that they prefer.(3) Consider a monthly sample of the water temperature in the Pacic oceanin a calendar year measured in celsius degrees.f 7: 2; 6: 7; 7: 3; 7: 3; 7: 7; 8: 2; 10: 1; 11: 3; 11: 2; 10: 0; 8: 8; 7: 5g What is the variance and standard deviation of this sample. Based onyour calculation would you consider a measurement of 5 degrees unusual ?would a measurement of 11.5 degrees be more or less likely in your opinion?Explain your reasoning.(4) Consider the list of annual rates of growth of an olive tree expressed inpercentiles.f 5; 4: 5; 4: 3; 5: 6; 3: 6g What would be the size of an olive tree which was 1 meter tall after 5 yearsof these growth rates ? (hint: after the rst year the height of the treewould be 1: 05 meters.)Express the growth rates in multiplicative factors. That is, the rst yearthe height of the tree is multiplied by 1.05 because it grows by 5%. Takethe geometric mean of the multiplicative growth rates. Why is that meanappropriate for this situation ?

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