Statistics
(1) Suppose you want to design a poll to predict the outcome of the presidential
elections. Explain how you would sample the population for the poll. Say
what type of sample would you use and explain specically how you would
design such a sample. Explain why such a sample is the appropriate one
for this situation.
(2) After describing your honest poll explain how a dishonest pollster can design
a 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 ocean
in 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 on
your 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 in
percentiles.
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 years
of these growth rates ? (hint: after the rst year the height of the tree
would be 1: 05 meters.)
Express the growth rates in multiplicative factors. That is, the rst year
the height of the tree is multiplied by 1.05 because it grows by 5%. Take
the geometric mean of the multiplicative growth rates. Why is that mean
appropriate for this situation ?