Suppose a hospital would like to estimate the proportion of patients who feel th

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 20 patients found that 14 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90% confidence interval with margin of error equal to 8% to estimate this proportion. The additional number of patients that need to be sampled is (Round up to the nearest integer.)

Explanation / Answer

Margin of Error, E = 8%, p = 14/20 = 0.7, z* = 1.64

N = p*(1-p)*(z/E)2 = 0.7*0.3*(1.64/0.08)2 = 88.25

Additional number required = 88.25 - 20 = 68.25 = 68

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