In: Statistics and Probability
In a study of 420,087 cell phone users, 108 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.
What is the test statistic?
What is the P-value?
What is the conclusion on the null hypothesis?
A.Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha .
B. Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha .
C.Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.
D.Reject the null hypothesis because the P-value is greater than the significance level, alpha
What is the final conclusion?
A. 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%.
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 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%.
D. 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%.
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.00034
Alternative hypothesis: P 0.00034
Note that these hypotheses constitute a two-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.001. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.000028444
z = (p - P) /S.D
z = - 2.92
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -2.92 or greater than 2.92.
Thus, the P-value = 0.0035
Interpret results. Since the P-value (0.0035) is greater than the significance level (0.001), we failed to reject the null hypothesis.
A) Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha .
A) 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%.