Question

In a survey of 4057 adults, 704 say they have seen a ghost. Construct 99 % confidence interval for the population proportion. Interpret your results.

Answer 1

Level of Significance,   α =    0.01
Number of Items of Interest,   x =   704
Sample Size,   n =    4057
      
Sample Proportion ,    p̂ = x/n =    0.1735

z -value =   "Zα/2 =2.5758
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0059
      
margin of error ,    E = Z*SE =    0.0153 [excel formula =normsinv(α/2) ]
      
Confidence Interval      
Interval Lower Limit , =    p̂ - E =    0.1582
Interval Upper Limit , =    p̂ + E =   0.1888

we are 99% confident that true population proportion who have seen a ghost will lie within confidence interval