Question

In a study of 346 comma 145 cell phone​ users, it was found that 26 developed cancer of the brain or nervous system. Assuming that cell phones have no​ effect, there is a 0.000113 probability of a person developing cancer of the brain or nervous system. We therefore expect about 40 cases of such cancer in a group of 346 comma 145 people. Estimate the probability of 26 or fewer cases of such cancer in a group of 346 comma 145 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous​ system?

Answer 1

Answer:

a) P ( X ≤ 26 ) = 0.0134

b) The significance of the cell phone causing brain cancer is 1.34 or 0.0134

Step-by-step explanation:

Solution:-

- From the entire population of cell phone users os size N = 346,145 media reported n = 26 people who developed cancer of brain or nervous system.

- The probability of a person developing cancer of the brain or nervous system, assuming that cell phones have no effect, is p = 0.000113.

- Denote a random variable X: The number people who developed cancer of brain or nervous system are normally distributed.

- The expected or mean number of people who developed cancer of brain or nervous system are u = 40.

- The standard deviation ( s ) for the distribution would be:

                          $s = \sqrt{u*( 1 - p ) }\\\\s = \sqrt{40*( 1 - 0.000113 ) }\\\\s = 6.3242$

- The random variate X follows normal distribution with parameters:

                         X ~ Norm ( 40 , 6.3242^2 )

- The probability of X ≤ 26 cases from the total population of N = 346,145 can be determined by evaluating the Z-score standard value of the test statistics:

                                     

                        $P ( X \leq 26 ) = P ( Z \leq [ \frac{X - u }{s} ) \\\\P ( Z \leq [ \frac{ 26 - 40 }{6.3242} ) = P ( Z \leq -2.21371 )$

- Using standard normal table compute the probability on the left side of Z-score value -2.21371. Hence,

                       P ( X ≤ 26 ) = 0.0134

- The probability of the less than 26 number of cases who developed cancer of the brain or nervous system is 0.0134 as per media reports.

- So 1.34% of population is a case brain cancer due to cell phones according to media reports.

Which is significant less than the expected number of cases ( 40 ) that occur regardless of cell phone effect.

Answer:  The significance of the cell phone causing brain cancer is 1.34 or 0.0134.