Question

A dean of a business school wanted to know whether the graduates of her school used the statistic skills that they learn in university during their first year of employment after graduation. As of today there are 34,050 graduates in total from the business school. The Dean is committed to allocate more funding to the development of the school’s statistics course if at least 17% of its graduates use statistics skills during their first year of employment. She surveyed 500 graduates. 105 graduates responded that they actually find the statistic skills they learnt in university useful and applicable in their first year of employment. Estimate with 95% confidence the proportion of all of the business school graduates who use their statistic skills during their first year of employment.

b) Obtain the 95% confidence interval estimate of the proportion of all of the business school graduates who use their statistic skills during their first year of employment. Display working.

Answer 1

Level of Significance,   α =    0.05          
Number of Items of Interest,   x =   105          
Sample Size,   n =    500          
                  
Sample Proportion ,    p̂ = x/n =    0.2100          
z -value =   Zα/2 =    1.960   [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.018215          
margin of error , E = Z*SE =    1.960   *   0.01822   =   0.0357
                  
95%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.21000   -   0.03570   =   0.174
Interval Upper Limit = p̂ + E =   0.21000   +   0.03570   =   0.246
                  
95%   confidence interval is (   0.1743   < p <    0.2457   )

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