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 2 percentage points with 95% confidence if he uses an estimate of 54% 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 2 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 a and b so close?

Explanation / Answer

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 2 percentage points with 95% confidence if he uses an estimate of 54% obtained from a poll?

The sample size is 2386 (Round up to the nearest integer)

Sample size

P=0.54

For 95%, z=1.96

d=0.02

Sample size = (z2*p*(1-p))/d2

= (1.962*0.54*0.46)/0.022

=2385.5

The sample size required= 2386

B)  What sample size should be obtained if he wants to be within 2 percentage points with 95% confidence if he does not use any prior estimates?

The sample size is 2401(Round up to the nearest integer)

Sample size

P=0.5 ( assumed)

For 95%, z=1.96

d=0.02

Sample size = (z2*p*(1-p))/d2

= (1.962*0.5*0.5)/0.022

=2400.9

The sample size required= 2401

C) Why are the results from a and b so close?

The estimate for p we used in first part a is 0.54 which is close to 0.5 we used in the second part b.

Therefore the results are close.

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