Question

Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 176 with 87 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

C.I. = _________

Answer 1

Given      
n = 176 …Sample Size     
p̂ = 87/176 = 0.4943  … Sample proportion of successes    
      
To find 80% confidence interval for population proportion p      
For 80%, α = 0.20, α/2 = 0.10      

From the z-tables, or Excel function NORM.S.INV(α/2)      
z = NORM.S.INV(0.10) = 1.96 = 1.282                 (We take the positive value for calculations)   

z = 1.282
Confidence interval is given by       

= (0.446, 0.543)      

C.I. = (0.446, 0.543)