Question 1201813: In a study of 420,113 cell phone users, 136 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 0.001significance 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 the binomial distribution.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 420,113 cell phone users.
136 developed cancer of the brain or nervous system.
sample p = 136 / 420,113 = .0003237224271.
population p assumed to be .034% / 100 = .00034.
standard error = sqrt (p * q / n) = sqrt (,99923 * (1 - .00034) / 420113) = .00002844346856.
test z-score = (sample mean minus assumed population mean) divided by standard error = (.0003237224271 - .00034) / .00002844346856 = -.5722780576.
area to the left of that = .2835667641.
that's greater than the critical p-value of .0005 (two tailed critical alpha is .001 / 2 = .0005 on each end), so the results are not considered significant.
the critical z-score on the low end was equal to -3.290526729.
the test z-score was considerably less than that, reinforcing the p-value concluson of no significance.
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