In a study of 420131 cell phone users 121 subjects developed

In a study of 420,131 cell phone users, 121 subjects developed cancer of the brain or nervous system. Test the claim of a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different from the rate of 0.0340% for people who do not use cell phones. Because this issue has such great importance, use a 0.005 significance level. Identify the null hypothesis, alternative hypothesis, test statistic, P-value conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to t he binomial distribution Which of the following is the hypothesis test to be conducted? OA. Ho:p#000034 ° C. Ho\' p:0.00034 OE. Ho\'p:0.00034 B. HOP > 0.00034 Ha p= 0.00034 D, Ho:p=0.00034 H1 p> 0.00034 F. Ho p

Solution

POPULATION PROPORTION Z TEST          
          
Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.00034
Ha:   p   =/=   0.00034 [OPTION E]

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As we see, the hypothesized po =   0.00034      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.000288005      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    2.84429E-05      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.83 [ANSWER, ITEM 2]

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As this is a    2   tailed test, then, getting the p value,  
          
p =    0.033772018 [ANSWER, ITEM 3]

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significance level =    0.005      
Comparing p and the significance value, we   FAIL TO REJECT THE NULL HYPOTHESIS. [OPTION C]

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It is option A. [THERE IS NO SUFFICIENT EVIDENCE THAT THE CLAIM IS TRUE.]