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)

Step-by-step 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 :

$p=\dfrac{134}{420000}\approx0.0032$

Significance level : $1-0.90=0.1$

Critical value : $z_{\alpha/2}=1.645$

The confidence interval for population proportion is given by :-

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

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).