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 18 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 95​% confidence interval with a margin of error equal to 3​% to estimate this proportion.

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin of Error, E = 0.03

The provided estimate of proportion p is, p = 0.45
The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:
n >= p*(1-p)*(zc/E)^2
n = 0.45*(1 - 0.45)*(1.96/0.03)^2
n = 1056.44

Therefore, the sample size needed to satisfy the condition n >= 1056.44 and it must be an integer number, we conclude that the minimum required sample size is n = 1057
Ans : Sample size, n = 1057 or 1056