A television sports commentator wants to estimate the proportion of citizens who

Question

A television sports commentator wants to estimate the proportion of citizens who "ollow professional football" Complete parts (a) through (c) (a) What sample size should be obtained if he wants to be within 3 percentage points weh 90% confidence if he uses an estimate of 54% obtined to a pr The sample size is 1165 (Round up to the nearest integer) (b) what sample size should be obtained if he wants to be within 3 percentage points with 96% confidence if he does not use any prior estimates? The sample size is 1164. (Round up to the nearest integer) (c) Why are the results from parts (a) and (b) so close? A. The results are close because the margin of emor 3% ís less than 5% O B. The results are close because 0 54(1-054)-0 2484 is very close to 0 25 o C. The results are close because the confidence 9g% is close to 100%.

Explanation / Answer

For no prior estimate of proportion we will take p = 0.5

So 0.5 * (1 - 0.5) = 0.25

For estimate of proportion p = 0.54

0.54 * (1 - 0.54) = 0.2484

0.2484 is very close to 0.25.

Option - B) The results are close because 0.54(1 - 0.54) = 0.2484 is very close to 0.25.

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