Question

A university would like to estimate the proportion of fans who purchase concessions at the first basketball game of the season. The basketball facility has a capacity of 3 comma 600 and is routinely sold out. It was discovered that a total of 200 fans out of a random sample of 500 purchased concessions during the game. Construct a​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game. The​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game is left parenthesis nothing comma nothing right parenthesis . ​(Round to three decimal places as​ needed.)

Answer 1

Level of Significance,   α =    0.05          
Number of Items of Interest,   x =   200          
Sample Size,   n =    500          
                  
Sample Proportion ,    p̂ = x/n =    0.400          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0219          
margin of error , E = Z*SE =    1.960   *   0.0219   =   0.0429
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.400   -   0.0429   =   0.3571
Interval Upper Limit = p̂ + E =   0.400   +   0.0429   =   0.4429
                  
so, confidence interval is (   0.357 < p <    0.443 )