A recent poll of 2200 randomly selected 18-25-year-olds revealed that 255 curren

Question

A recent poll of 2200 randomly selected 18-25-year-olds revealed that 255 currently use marijuana or hashish. According to a publication, 12.5 % of 18-25-year-olds were current users of marijuana or hashish in 1997. Do the data provide sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%? Use =0.05significance level.

test statistic z=

positive critical z score   

negative critical z score    

The final conclusion is

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.125
Ha:   p   =/=   0.125
As we see, the hypothesized po =   0.125      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.115909091      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.007050951      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.289316742   [ANSWER, TEST STATISTIC]

*******************************  
          
As this is a    2   tailed test, then, the critical z values at 0.05 level are

positive critical z score = 1.96 [answer]
negative critical z score = -1.96 [answer]
          
As |z| < 1.96, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Hence, there is no significant evidence that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%. [CONCLUSION]

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