Question

An advertising agency wishes to estimate,

within

95% confidence and to

within

two percentage po

ints, the

proportion

of all adults who recognize its

client’s logo. Knowing that two years ago the proportion was 19%, then the

estimated minimum

sample size

needed is

(a)

2401

(b)

1042

(c)

1479

(d)

966

(e)

1566

Answer #1

Solution :

Given that,

= 0.19

1 - = 1 - -0.19 = 0.81

Margin of error = E = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2} =
Z_{0.025} = 1.96

Sample size = ( Z_{/2} /
E)^{2} * * (1 - )

= (1.96 / 0.02)^{2} * 0.19 * 0.81

= 1478.05

Sample size = n = 1479

Option C) Is correct .

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