Question

11.

In a study of 420,055 cell phone​ users, 150 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 0.005 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.

________________________

Which of the following is the hypothesis test to be​ conducted?

A.

H0: p>0.00034

H1: p=0.00034

B.

H0: p≠0.00034

H1: p=0.00034

C.

H0: p<0.00034

H1: p=0.00034

D.

H0: p=0.00034

H1: p≠0.00034

E.

H0: p=0.00034

H1: p<0.00034

F.

H0: p=0.00034

____________________

What is the test​ statistic?

z= ​(Round to two decimal places as​ needed.)

What is the​ P-value?

​P-value=  ​(Round to four decimal places as​ needed.)

________________________

What is the conclusion on the null​ hypothesis?

A.

Reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

α.

B.

Reject

the null hypothesis because the​ P-value is

greater than

the significance​ level,

α.

C.

Fail to reject

the null hypothesis because the​ P-value is

less than or equal to

the significance​ level,

α.

D.

Fail to reject

the null hypothesis because the​ P-value is

greater than

the significance​ level,

α.

______________

What is the final​ conclusion?

A.There

is

sufficient evidence to warrant rejection of 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%.

B.There

is not

sufficient evidence to warrant rejection of 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%.

C.There

is

sufficient evidence to support 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%.

D.There

is not

sufficient evidence to support 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%.

Answer 1

Solution :

Given that,

= 0.00034

1 - = 0.99966

n = 420055

x = 150

Level of significance = = 0.005

Point estimate = sample proportion = = x / n = 0.00040

This a two- tailed test.

The null and alternative hypothesis is,

D)

Ho: p = 0.00034

Ha: p 0.00034

Test statistics

z = ( - ) / *(1-) / n

= ( 0.00040 - 0.00034) / (0.00034*0.99966) / 420055

= 0.60

P-value = 2 * P(Z > z )

= 2 * ( 1 - P(Z < 0.60 ))

= 0.5486

Therefore,

D.

Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, α.

D.

There is not sufficient evidence to support 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%.