Question

A study of 420,047 cell phone users found that 130 of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0223​% for those not using cell phones. Complete parts​ (a) and​ (b). a. Use the sample data to construct a 90​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell​ phones? Why or why​ not?

A. No, because 0.0223​% is not included in the confidence interval.

B.No​, because 0.0223% is included in the confidence interval.

C. Yes, because 0.0223% is included in the confidence interval.

D. Yes, because 0.0223​% is not is not included in the confidence interval.

Answer 1

Solution :

a) The 90% confidence interval for population percentage is given as follows :

Where, p̂ is sample percentage, q̂ = 100 - p̂, n is sample size and Z(0.10/2) is critical z-value to construct 90% confidence interval.

Sample percentage of cellphone users who developed cancer of the brain or nervous system is given by,

n = 420047

Using Z-table we get, Z(0.10/2) = 1.645

Hence, 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system is,

The 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system is (0.02648%, 0.03541%).

b) Since, 0.0223% is not included in the sample, therefore we can conclude that the cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell​ phones.

Hence, option (D) is correct.

Please rate the answer. Thank you.