An article in Fortune newspaper claimed that nearly half of all engineers contin

Question

An article in Fortune newspaper claimed that nearly half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving an M.S. or a PhD. degree. Data from an article in Engineering Horizons indicated that 117 of 484 new engineering graduates were planning graduate study.

Are the data from engineering Horizons consistent with the claim reported by Fortune? Use = 0.05 in reaching your conclusions. Find the P-value for this test.

Discuss how you could have answered part (a) above by constructing a two sided confidence interval on p

Explanation / Answer

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.5
Ha:   p   =/=   0.5
As we see, the hypothesized po =   0.5      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.241735537      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.022727273      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -11.36363636      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    6.34475E-30   [ANSWER, P VALUE]  

significance level =    0.05      

As P < 0.05, we   REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence that not nearly half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving an M.S. or a PhD. degree at 0.05 level. [CONCLUSION]

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b)

We could have constructed a 95% confidence interval, and inspect if the interval contains 0.5, then we do not reject the null hypothesis. We reject Ho if the interval does not contain 0.5.

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