Question

Giving a test to a group of students, the grades and gender are summarized below

A B C Total

Male 18 16 6 40

Female 13 19 15 47

Total 31 35 21 87

Let p represent the population proportion of all female students who received a grade of B on this test. Use a 99% confidence interval to estimate p to four decimal places if possible. < p <

Answer 1

Level of Significance,   α =    0.01          
Number of Items of Interest,   x =   19          
Sample Size,   n =    47          
                  
Sample Proportion ,    p̂ = x/n =    0.404         
z -value =   Zα/2 =    2.576   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0716          
margin of error , E = Z*SE =    2.576   *   0.0716   =   0.1844
                  
99%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.404   -   0.1844   =   0.2199
Interval Upper Limit = p̂ + E =   0.404   +   0.1844   =   0.5886
                  
99%   confidence interval is (   0.2199   < p <    0.5886   )

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