Question

Suppose a hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 22 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 99​% confidence interval with a margin of error equal to 8​% to estimate this proportion.

the additional patients that need to be sampled is ____

Answer 1

Solution :

Given that,

n = 40

X = 22

$\hat p$ = X / n = 22 / 40 = 0.55

1 - $\hat p$ = 1 - 0.55 = 0.45

margin of error = E = 8% = 0.08

At 99% confidence level the z is ,

$\alpha$ = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

Z _{$\alpha$ /2} = Z_0.005 = 0.502

sample size = n = (Z _{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= (0.502/ 0.08)² * 0.55*0.45

= 9.75

sample size = 10