Question

Determine the margin of error for a 98​% confidence interval to estimate the population proportion with a sample proportion equal to 0.80 for the following sample sizes.

a. n equals125             b. n equals200             c. n equals250

The margin of error for a 98​% confidence interval to estimate the population proportion with a sample proportion equal to 0.80 and sample size n equals=125 is nothing

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.80

1 - = 1 - 0.80 = 0.20

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

Z/2 = Z0.01  = 2.326

a) n = 125

Margin of error = E = Z / 2 * (( * (1 - )) / n)

E = 2.326 (((0.80 * 0.20) / 125 )

E = 0.083

b) n = 200

Margin of error = E = Z / 2 * (( * (1 - )) / n)

E = 2.326 (((0.80 * 0.20) / 200 )

E = 0.066

c) n = 250

Margin of error = E = Z / 2 * (( * (1 - )) / n)

E = 2.326 (((0.80 * 0.20) / 250 )

E = 0.059