Question

In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported by US Today). The claim is that cell phone users develop cancer of the brain or nervous system at a rate that is greater than the rate of 0.034% (0.00034) for people that do not use cell phones.

1. What can you conclude by comparing the 95% Confidence Interval and the rate of cancer of the brain or nervous system for non-cell phone users? Justify your answer.

2. In performing a formal test of hypothesis to determine if the use of cell phones increase the rate development of brain or nervous system cancers, the form hypotheses are:

3. Using the cell phone brain and nervous system cancer rate information from above, find the appropriate critical standard normal z-value for performing the test of hypothesis.

4. Perform the formal test of hypothesis and obtain the z-calc value to see if using cell phones increases the rate of the development of brain or nervous system cancers using the information from above.

5. Compare z-critical and z-calc and draw the appropriate conclusion for this test of hypothesis. Justify your answer.

Answer 1

Solution-1:

p^=sample proprtion cell phone users develop cancer of the brain or nervous system=x/n=135/420095= 0.0003213559

n=420095

zc rit for 95% =1.96

95% confidence interval for p,population proportion of cell phone users develop cancer of the brain or nervous system

p^-z*sqrt(p^*(1-p^)/n),p^+z*sqrt(p^*(1-p^)/n)

0.0003213559-1.96*sqrt(0.0003213559*(1-0.0003213559)/420095),0.0003213559+1.96*sqrt(0.0003213559*(1-0.0003213559)/420095

0.0002671551,0.0003755567

0.0002671551<p<0.0003755567

Solution-2:

Null hpothesis:Ho:p=0.00034

Alternative Hypothesis,Ha:p>0.00034

3. Using the cell phone brain and nervous system cancer rate information from above, find the appropriate critical standard normal z-value for performing the test of hypothesis.

critical z value in excel

=NORM.S.INV(0.05)

=1.644853627

4. Perform the formal test of hypothesis and obtain the z-calc value to see if using cell phones increases the rate of the development of brain or nervous system cancers using the information from above.

z=p^-p/sqrt(p*(1-p)/n

=(0.0003213559-0.00034)/sqrt(0.00034*(1-0.00034)/420095)

z=-0.6554651

5. Compare z-critical and z-calc and draw the appropriate conclusion for this test of hypothesis. Justify your answer.

z=-0.6554651

Z<Zc

-0.6554651<1.644853627

Do not reject Null hypothesis

Accept null hypothesis.

There is no sufficient evidence at 5% level of significance to conclude that cell phones increases the rate of the development of brain or nervous system cancers.