Question

A simple random sample of 500 elements generates a sample proportion p = 0.72 

a. Provide the 99% confidence interval for the population proportion (to 4 decimals).

(    , )

b. Provide the 90% confidence interval for the population proportion (to 4 decimals).

( , )

Answer 1

a)

Level of Significance,   α =    0.01  
Sample Size,   n =    500  
          
Sample Proportion ,    p̂ =    0.720  

z -value =   "Zα/2 =
"   2.5758   [excel formula =NORMSINV(α/2)]

Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0201  
          
margin of error ,    E = Z*SE =    0.0517  
          
Confidence Interval          
Interval Lower Limit , =    p̂ - E =    0.6683
Interval Upper Limit , =    p̂ + E =   0.7717   

b)

Level of Significance,   α =    0.1  
Sample Size,   n =    500  
          
Sample Proportion ,    p̂ =    0.720  
z -value =   "Zα/2 =
"   1.6449   [excel formula =NORMSINV(α/2)]

Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0201  
          
margin of error ,    E = Z*SE =    0.0330  
          
Confidence Interval          
Interval Lower Limit , =    p̂ - E =    0.6870  
Interval Upper Limit , =    p̂ + E =   0.7530