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 50 patients found that 36 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90​% confidence interval with a margin of error equal to 8​% to estimate this proportion.

The additional number of patients that need to be sampled is _____.

Answer 1

Solution :

Given that,

n = 50

x = 36

Point estimate = sample proportion = = x / n = 36 / 50 = 0.72

1 - = 1 - 0.72 = 0.28

margin of error = E = 0.08

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.08)2 * 0.72 * 0.28

= 85.23

sample size = n = 86