Find the appropiate confidence interval 938 CI for proportio

Find the appropiate confidence interval:

93.8% CI for proportion with n = 27, sample proportion = 0.4.

Solution

Given: n = 27, sample proportion = 0.4

When the true population proportion is not known, the Standard error(SE) provides an unbiased estimate of the standard deviation. The SE is given by the equation,

SE_p = sqrt[ p *( 1-p)/n ]

Where p is the sample proportion and n is the sample size.

SE_p = sqrt[ 0.4 * (1-0.4) / 27 ]

= sqrt(0.008) = 0.089

Given the confidence interval = 93.8%, therefore from the table the value of Z[P(1-0.062/2) will be 1.866.

Margin of error = critical value * standard error of the statistic

= 1.866 * 0.089 = 0.166~ 0.17

The range of the confidence interval is given by the sample statistic plus or minus Margin of Error.And the uncertainity is denoted by the confidence level.

Therefore 93.8% confidence interval is 0.23 - 0.57and the range of the interval is given by 0.4+- 0.17