In a study of 420,080 cell phone users, 138 subjects developed cancer of the bra
ID: 3335723 • Letter: I
Question
In a study of 420,080 cell phone users, 138 subjects developed cancer of the brain or nervous system. 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 0.001 significance level. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.
Find Null Hypothesis and Alternative Hypothesis
b. What is the test statistic? z= _______ (Round the final answer to two decimal places as needed.)
c. What is the P-value? P-value= ________ (Round to four decimal places as needed.)
d. What is the conclusion?
A. There is sufficient evidence to support the claim. B. There is not sufficient evidence to support the claim
e. Is the conclusion valid today? Why or why not?
A. Yes, the conclusion is valid
B. No, the conclusion is not valid
C. You can make no decisions about the validity of the conclusion
Explanation / Answer
Given that,
possibile chances (x)=138
sample size(n)=420080
success rate ( p )= x/n = 0.0003
success probability,( po )=0.00034
failure probability,( qo) = 0.99966
null, Ho:p=0.00034
alternate, H1: p( not equal ) 0.00034
level of significance, = 0.001
from standard normal table, two tailed z /2 =3.29
since our test is two-tailed
reject Ho, if zo < -3.29 OR if zo > 3.29
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.00033-0.00034/(sqrt(0.0003398844)/420080)
zo =-0.404
| zo | =0.404
critical value
the value of |z | at los 0.001% is 3.29
we got |zo| =0.404 & | z | =3.29
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.40398 ) = 0.68622
hence value of p0.001 < 0.6862,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.00034
alternate, H1: p!=0.00034
b.
test statistic: -0.404
c.
p-value: 0.68622
d.
A. There is sufficient evidence to support the claim
we have evidence that cell phone users develop cancer of the brain or nervous
system at a rate that is similar to 0.0340% for people who do not use cell phones
e.
A. Yes, the conclusion is valid