Question

A study of 420 comma 093 cell phone users found that 137 of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0311​% for those not using cell phones. Complete parts​ (a) and​ (b).

a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

_%<p< _​% ​(Round to three decimal places as​ needed.)

b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell​ phones? Why or why​ not?

Answer 1

a)

sample success x =		137
sample size          n=		420093
sample proportion p̂ =x/n=		0.000326
std error se= √(p*(1-p)/n) =		0.000028
for 90 % CI value of z=		1.645
margin of error E=z*std error   =		0.0000
lower bound=p̂ -E                       =		0.00028
Upper bound=p̂ +E                     =		0.00037

0​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system =0.028 % < p <0.037 %

b)

since interval values contain 0.0311% as plausible value of population proportion, the rate does not appear to be different,