A dean of a business school wanted to know whether the graduates of her school u

Question

A dean of a business school wanted to know whether the graduates of her school used a statistical inference technique during their first year of employment after graduation. She surveyed 314 graduates and asked about the use of statistical techniques. After tallying the responses, she found that 204 used statistical inference within one year of graduation. Estimate with 90% confidence the proportion of all business school graduates who use their statistical education within a year of graduation. show each step of your work.

Explanation / Answer

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.649681529          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.026922597          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.044283732          
lower bound = p^ - z(alpha/2) * sp =   0.605397797          
upper bound = p^ + z(alpha/2) * sp =    0.69396526          
              
Thus, the confidence interval is              
              
(   0.605397797   ,   0.69396526   ) [ANSWER]

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