In a study of 420095 randomly selected Danish cell phone use

In a study of 420,095 randomly selected Danish cell phone users, 135 subjects developed cancer of the brainn or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today). Test the claim of a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different from the rate of 0.0340% for people who do not use cell phones. Because this issue has such great importance, use a .005 significance level. Conduct this test by following the steps below:

a. Give the apporpriate hypotheses for this test and define any parameters used.

b. List and Verify conditions for the appropriate hypothesis test

c. Give the apporpriate test statistic. Show formula, work and value

d. Find the appropriate p-value. Draw an appropriate picture, show work, and give the value to 4 decimal places.

e. What is your decision regarding the null hypothesis?

f. What are your conclusions about this particular test?

Solution

Set Up Hypothesis
Null, cell phone users develop cancer of the brain or nervous system at a rate that is similar H0:P=0.034
Alternate, cell phone users develop cancer of the brain or nervous system at a rate that is different H1: P!=0.034
Test Statistic
No. Of Success chances Observed (x)=135
Number of objects in a sample provided(n)=420095
No. Of Success Rate ( P )= x/n = 0.0003
Success Probability ( Po )=0.034
Failure Probability ( Qo) = 0.966
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.00032-0.034/(Sqrt(0.032844)/420095)
Zo =-120.4482
| Zo | =120.4482
Critical Value
The Value of |Z | at LOS 0.005% is 2.81
We got |Zo| =120.448 & | Z | =2.81
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -120.44821 ) = 0
Hence Value of P0.005 > 0,Here we Reject Ho

We conclude that cell phone users develop cancer of the brain or nervous system at a rate that is different