Atelevision sports commentator wants to estimate the proportion of citizens who "follow professional football." complete parts (a) through (c).

Part A

The number of samples needed to get a confidence interval with a margin of error M is given by:



where is the z-score of the confidence level and p is the population proportion.

If he wants to be within 4 percentage points with 96% confidence and he uses an estimate of 48% obtained from a poll, the sample size that should be obtained is given by:



Part B:

If he wants to be within 4 percentage points with 96% confidence and he does not use any prior estimates, the sample size that should be obtained is given by:



Part C:

The resulta from parts a and b are close because the result from the poll (i.e. 48%) is close to the conservative proportion used when there is no prior knowledge of any proportion (i.e. 50%).