Voters Poll. A polling agency wants to determine the size of a random sample nee

Question

Voters Poll. A polling agency wants to determine the size of a random sample needed to estimate the percentage of voters that Candidate X will receive in the next city council election in a mid-sized city. The estimate should have a margin of error of no more than 1.5 percentage points at 95% level of confidence. (7.65) a. How large a sample should the agency take? Because a 95% interval is desired, use the shortcut formula: n = 1/m^2. Recall that for this formula, the margin of error must be in decimal form. b. Would a 1% margin of error require a larger or smaller sample than in part (a)? c. If the degree of confidence were lowered to 90%, with the margin of error no more than 1.5%, would that require a larger or smaller sample size than the result for part (a)?

Explanation / Answer

(a) n = 1/m^2 = 1/0.015^2 = 4445

(b) A 1% margin of error will require a much larger sample

(c) If the degree of confidence were lowered to 90%, it will require a much smaller sample.

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