Question

a random sample of 127 people were randomly samoled, 44 were found to be infected with the virus.

find the upper limit of of a 94% confidence interal for the true proportion of people that are infected.

Answer 1

Sample size , n= 127

Sample proportion of people that are infected, $\hat{p}$ = 44/127 = 0.3465

94% Confidence interval for the true population of people that are infected

=( $\hat{p} \pm Z_{0.06/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ )

=( $0.3465 \pm 1.88\sqrt{\frac{0.3465(1-0.3465)}{127}}$ )

=( $0.3465 \pm 0.0794$ )

=( 0.2671, 0.4259)

Upper limit of of a 94% confidence interal = 0.4259