Some people are concerned that the new tougher standards and

Some people are concerned that the new tougher standards and high stakes tests adopted in many states have driven up the high school drop out rate. That national center for education statistics reported that the high school dropout rate for the year 2004 was 10.3%. One school district whose dropout rate was always very close to the national average reports that 210 out of 1782 high school students dropped out last year. Is this evidence that their dropout rate may be increasing? Explain.

1.) Hypotheses

2.) Test Statistic

3.)P-value

4.) Conclusion. interpret your conclusion in context of the problem.

I have most of it but double checking. Thanks.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.103
Ha:   p   >   0.103 [ANSWER, HYPOTHESES]
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As we see, the hypothesized po =   0.103      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.117845118      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.007200472      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    2.061686682 [ANSWER, TEST STATISTIC]      
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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.019618788       [ANSWER, P VALUE]
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significance level =    0.05      

Comparing p < 0.05, we   REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the dropout rate increased. [CONCLUSION]