Question

this region A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 5 percentage points with 90% confidence if 5. he uses a previous estimate of 38% b. he does not use any prior estimates? Page 4 of 4

Answer 1

(a) The ME = Zcritical * SQRT(p * q/n).

Squaring and solving, n = (Zc/ME)² * p * q

Here ME = 0.05, p = 0.38 (38%), q = 1 - p = 0.62

The Zc at $\alpha$ = 0.10 is 1.645

Therefore n = (1.645/0.05)² * 0.38 * 0.62 = 255.02

Therefore n = 256 (Rounding to the nearest Integer)

(b) Here p = 0.5, q = 1 - p = 0.5, since no prior estimate is available

The Zc at $\alpha$ = 0.10 is 1.645

Therefore n = (1.645/0.05)² * 0.5 * 0.5 = 270.6

Therefore n = 271 (Rounding to the nearest Integer)