According to US News and world Report, from a random sample of 794 medical stude

Question

According to US News and world Report, from a random sample of 794 medical students at UT southwestern during the 1998-1999 school year 46% of these students were women. The US Census Bureau says that 51% of the residents of the USA are female. Are female medical students at UT southwestern underrepresented relative to the US population? Set up the null and alternative hypothesis Calculate the test statistic Calculate the p-value. Make and justify a statistical decision (). State your conclusions in context of the problem.

Explanation / Answer

8.

1.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.51
Ha:   p   <   0.51 [ANSWER]

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2.
As we see, the hypothesized po =   0.51      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.46      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.017740787      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.81836429   [ANSWER]

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3.  
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.002413451   [ANSWER]

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4.

As the Pvalue is very small, we reject Ho.

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5.

There is significant evidence that the female medical students at UT Southwestern are underrepresented relative to the US population. [CONCLUSION]

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