Question

For the qualitative data, choose one of the outcomes and find the sample proportion satisfying that outcome. Now construct a 95% Confidence Interval of the Population Proportion of people satisfying that outcome.

Gender	Frequency
Male	3
Female	36
Both Genders 50/50	10

Data Description: So there were 49 states counted for and of that 49 there were 3 states where the male population was greater than the females and there were 36 states where the female population was greater than the males and lastly there were 10 states where both populations were equal.

Answer 1

let choose sample of female where there were 36 states where the female population was greater than the males

so,

Level of Significance,   α =    0.05          
Number of Items of Interest,   x =   36          
Sample Size,   n =    49          
                  
Sample Proportion ,    p̂ = x/n =    0.735          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0631          
margin of error , E = Z*SE =    1.960   *   0.0631   =   0.1236
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.735   -   0.1236   =   0.6111
Interval Upper Limit = p̂ + E =   0.735   +   0.1236   =   0.8583
                  
so, 95% confidence interval is (   0.6111   < p <    0.8583   )