Question

A study of 420,059 cell phone users found that 135 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 0.0314​% for those not using cell phones. Complete parts​ (a) and​ (b).

a)Use the sample data to construct a

95​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

b) do cell phone users appear to have a rate of 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

Answer)

N = 420,059

P = 135/420059

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 135

N*(1-p) = 419924

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 95% confidence level is 1.96

Margin of error (MOE) = Z*√{P*(1-P)}/√N

MOE = 0.00542054385%

Interval is given by

(P-MOE, P+MOE)

(0.0267%, 0.0376%)

B)

Null hypothesis Ho : P = 0.0314

Alternate hypothesis Ha : P not equal to 0.0314

As the obtained interval contains the null hypothesised value 0.0314

We fail to reject the null hypothesis Ho

So, we do not have enough evidence to conclude that p is not equal to 0.0314