Question

A study of 420 comma 000 cell phone users found that 134 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 0.0438​% for those not using cell phones. 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.

Answer 1

Answer: (0.00306,0.00334)

Explanation:

Given : Sample size : n= 420000

The number of users developed cancer of the brain or nervous system =134

Then , the proportion of users developed cancer of the brain or nervous system :

`p=(134)/(420000)\approx0.0032`

Significance level :
`1-0.90=0.1`

Critical value :
`z_(\alpha/2)=1.645`

The confidence interval for population proportion is given by :-

`p\ \pm\ z_(\alpha/2)\sqrt{(p(1-p))/(n)}\\\\=0.0032\pm (1.645)\sqrt{((0.0032)(1-0.0032))/(420000)}\approx0.0032\pm0.00014\\\\=(0.00306,0.00334)`

Hence, the 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system is (0.00306,0.00334).