In a study of 420,063 cell phone users, 138 subjects developed cancer of the bra
ID: 3149402 • Letter: I
Question
In a study of 420,063 cell phone users, 138 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 0.001 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 the binomial distribution.
A) What is the test statistic
B) Determine the p-value
Explanation / Answer
H0: Pu=0.00034
H1: Pu not equal to 0.00034
A) For single, sample proportions, large samples, use 1-proportion z test.
Z=(Ps-Pu)/sqrt {Pu(1-Pu)/N}=(0.00033-0.00034)/sqrt {(0.00034*0.99966)/420063}=-0.35
Ps is the sample proportion, 138/420063, and Pu is the population proportion, 0.00034 and N is the sample size, 420063.
B) The p value is 0.363. The p value is not less than 0.001, therefore, fail to reject null hypothesis. The claim is not significant at alpha=0.001 level.