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 "follow professional football". Complete parts (a) through (c).

(a) What sample size should be obtained if he wants to be within 3 percentage points with 95% confidence if he uses an estimate of 48% obtained from a poll?

The sample size is ___. (round up to the nearest integer.)

(b) What sample size should be obtained if he wants to be within 3 percentage points with 95% confidence if he does not use any prior estimates?

The sample size is ___. (round up to the nearest integer.)

(c) Why are the results from parts (a) and (b) so close?

1. The results are close because 0.48(1-0.48)=0.2496 is very close to 0.25

2. The results are close because the margin of error 3% is less than 5%

3. The results are close because the confidence 95% is close to 100%

Explanation / Answer

a)

sample size n = Z2 p(1-p) / E2

= 1.962 * 0.48 * 0.52 / 0.032

= 1065.4

n = 1066

b)

sample size n = Z2 p(1-p) / E2

= 1.962 * 0.50 * 0.50 / 0.032

= 1067.11

n = 1068

c)

The  results from parts (a) and (b) so close because,

Proportions 0.48(1-0.48)=0.2496 is very close to 0.25.

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