Question

It is estimated that a candidate has 40 percent support in a population. What minimum sample size should be used to construct a 90 percent confidence interval with a maximum width of 0.1

Answer 1

Solution:

Given,

p = 40% = 0.40

1- p = 1 - 0.40 = 0.60

Width of interval = 0.1

Margin of error = E = width/2 = 0.1/2 = 0.05

c = 90% = 0.90

Now,

= 1 - c = 1 - 0.90 = 0.10

/2 = 0.05

= 1.645  (using z table)

The sample size for estimating the proportion is given by

n =

= (1.645)² * 0.4 * 0.6 / (0.05²)

= 259.7784

= 260 ..(round to the next whole number)

Answer : 260