SOLUTION: 14.A group of investigators wishes to explore the relationship between the use of hair dyes and the development of breast cancer in females. A group of 1000 beauticians 40 - 49 y

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Question 1200100: 14.A group of investigators wishes to explore the relationship between the use of hair dyes and the development of breast cancer in females. A group of 1000 beauticians 40 - 49 years of age is identified and followed for five years. After five years, 20 new cases of breast cancer have occurred. Assume that breast cancer incidence over this time period for average American women in this age group is 7/1000. Test the hypothesis that using hair dyes increases the risk of breast cancer. Use ( =0.05).
Answer by Theo(13342) About Me  (Show Source):
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population ratio is assumed to be 7/1000 = .007
sample size is 1000.
sample ratio is 20/1000 = .02
standard error is ( population p * population q / 1000) ^ .5 = (7/1000 * (1 - 7/1000) / 1000) ^ .5 = .0026364749
population mean is assumed to be 7/1000 = .007
sample mean is 20/1000 = .02
z-score = (sample mean minus population mean) / standard error = (.02 - .007) / .0026364749 = 4.9308
critical z-score at two tailed 95% confidence interval = plus or minus 1.96.
since the test z-score is well above that, then it is asssumed that the use of the hair dye is most probability associated with an increase in the incidences of breast cancer.