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 ?