Question

In a study of 420,017 cell phone users,180 subjects developed brain cancer. Test the claim that cell phone users develop brain cancer 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. Use this information to answer the following questions.

What is the test​ statistic?

What is the​ P-value?

Answer 1

GIVEN:

Sample size of cell phone users

Number of cell phone users who developed brain cancer

HYPOTHESIS:

The hypothesis is given by,

(That is, cell phone users develop brain cancer at a rate that is not significantly different from the rate of 0.0340% for people who do not use cell phones.)

(That is, cell phone users develop brain cancer at a rate that is significantly different from the rate of 0.0340% for people who do not use cell phones.)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows standard normal distribution

where

is the sample proportion of cell phone users who developed brain cancer

is the hypothesized value .

CALCULATION:

The sample proportion of cell phone users who developed brain cancer is,

Now,

  

  

Thus the test statistic is .

P VALUE:

The two tailed p value for the calculated z score is,

  

Using the z table, the probability value is the value with corresponding row 3.2 and column 0.01.

  

  

  

Thus the calculated p value is .

DECISION RULE:

CONCLUSION:

Since the calculated p value (0.0014) is less than the significance level , we reject null hypothesis and conclude that cell phone users develop brain cancer at a rate that is significantly different from the rate of 0.0340% for people who do not use cell phones.