Question

How do I find the Confidence Levels and Margin of Error in Excel for the below?

Sample size=200

Poor room quality: P = 42/200 = 0.21

Poor food quality: P = 47/200 = 0.235

Poor service quality: P= 54/200 = 0.27

92% confidence interval for proportion of all clients who answerd "Poor" to room quality

Answer 1

here p=0.21 , n=200

for standard error of proportion =√(p(1-p)/n)

since 92$ middle values are between 4th and 96th percentile :

from excel :

margin of error =z*standard deviation =normsinv(0.96)*sqrt(0.21*(1-0.21)/200) =0.0504

lower confidence bound =estimated proportion -margin of error =0.21-0.0504 =0.1596

upper confidence bound =estimated proportion+margin of error =0.21+0.0504 =0.2604

therefore 92% confidence interval for proportion of all clients who answerd "Poor" to room quality

=(0.1596 to 0.2604)

(please reply if further clarification is required)