Question

Suppose it’s 1974, and you’re working as a pollster. You want to figure out how many people you’d have to survey to get a 97.5% confidence interval of ±4% for the proportion of Americans who say baseball is their favorite sport.

(a) Find an appropriate sample size assuming you have no previous information.

(b) Now suppose that your helpful intern has found a Gallup poll from 1972 in which 19% of Americans surveyed said that baseball was their favorite sport.4 Use this information to find an appropriate sample size.

Answer 1

Part a

The sample size formula is given as below:

n = p*q*(Z/E)^2

We are given not given estimate for proportion, so we take

p = 0.5

q = 1 – p = 0.5

Confidence level = 97.5%

Critical Z value = 2.2414

(by using z-table)

Margin of error = E = 0.04

The sample size is given as below:

n = p*q*(Z/E)^2

n = 0.5*0.5*(2.2414/0.04)^2

n = 784.9803

Required sample size = 785

Part b

The sample size formula is given as below:

n = p*q*(Z/E)^2

We are given

p = 0.19

q = 1 – p = 0.81

Confidence level = 97.5%

Critical Z value = 2.2414

(by using z-table)

Margin of error = E = 0.04

The sample size is given as below:

n = p*q*(Z/E)^2

n = 0.19*0.81*(2.2414/0.04)^2

n = 483.2339

Required sample size = 484