A recent study conducted by the state government attempts to determine whether t

Question

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than 0.66. At = 0.10:

   Select which null and alternate is correct.
   H_0:p1200 , H_a:p>1200
   H_0:p1500 , H_a:p>1500
   H_0:p0.66 , H_a:p>0.66
   H_0:<0.66 , H_a:P0.66

   At =0.10 what is the “test statistic”?

   What is the “critical value”?

   What is the conclusion of the hypothesis test and why?

Explanation / Answer

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.66
Ha:   p   >   0.66 [ANSWER, C]

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b)

As we see, the hypothesized po =   0.66      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.68      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.012231108      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.63517485   [ANSWER, TEST STATISTIC]

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c)

As this is right tailed, 0.10 level,

zcrit = 1.28 [ANSWER]

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d)  
          
As z > 1.28, we   REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence that the proportion of citizens supporting an increase in cigarette taxes is significantly greater than 0.66. [CONCLUSION]

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