Question

A simple random sample of 1000 elements generates a sample proportion p =0.68  

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

(     , )

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

( , )

Answer 1

CONFIDENCE INTERVAL IS NOT GIVEN SO WE ASSUME FOR PART A-99% AND FOR PARTB-90%

a)

Level of Significance,   α = 1- 0.99= 0.01  
Sample Size,   n =    1000  
          
Sample Proportion ,    p̂ =    0.68

z -value =   "Zα/2 = 2.5758 FROM CRITICAL VALUE TABLE

Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.01475

margin of error ,    E = Z*SE =    0.0380

Confidence Interval          
Interval Lower Limit , =    p̂ - E =    0.6420
Interval Upper Limit , =    p̂ + E =   0.7180

b)

Level of Significance,   α =1- 0.90 = 0.1  
Sample Size,   n =    1000  
          
Sample Proportion ,    p̂ =    0.68
z -value =   "Zα/2 =1.6449

Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.01475
          
margin of error ,    E = Z*SE =    0.0243
          
Confidence Interval          
Interval Lower Limit , =    p̂ - E =    0.6557
Interval Upper Limit , =    p̂ + E =   0.7043