A study of 420,095 Danish cell phone users found that 135 of them developed canc
ID: 3363165 • Letter: A
Question
A study of 420,095 Danish cell phone users found that 135 of them developed cancer of the brain or nervous system. The data are from the Journal of the National Cancer Institute. Construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.
b) It was found that 77 cell phone user, in this study, developed leukemia. At = 0.01, is there enough evidence that cell phone users have a leukemia rate that is greater than 0.019%? Use both the p-value and the rejection point methods.
Explanation / Answer
Ans:
a)sample proportion=135/420095=0.00032
z value for 95% CI is 1.96
95% confidence interval for p
=0.00032+/-1.96*sqrt(0.00032*(1-0.00032)/420095)
=0.00032+/-0.000054
=(0.00027,0.00038)
b)
sample proportion=77/420095=0.000183
H0:p<=0.00019
Ha:p>0.00019
critical z value=2.33
reject H0,if z>2.33
standard dev=sqrt(0.00019*(1-0.00019)/420095)=0.000213
Test statistic:
z=(0.000183-0.00019)/0.000213=-0.315
p-value(z>-0.315)=0.6236
As,p-value>0.01,we fail to reject null hypothesis.
(or z<2.33,we fail to reject null hypothesis.)
There is not enough evidence to conclude that cell phone users have a leukemia rate that is greater than 0.019%.
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