A study of 420,063 cell phone users found that 130 of them developed cancer of t

Question

A study of 420,063 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 0323% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 95% confidence interval estimate of the percentage or cell phone users who develop cancer of the brain or nervous system. Round to three decimal places as needed.) 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 b. Do cell phone using cell phones? Why or why not? o A. No, because 0 0323% is not included in the confidence interval B. Yes, because 0323% is not included in the confidence interval O c. No, because 0 0323% is included in the confidence interval. O D. Yes, because 0 0323% is included in the confidence interval.

Explanation / Answer

Here sample proportion

p^ = 130/420063 = 3.0948 x 10-4 = 0.030948 %

standard error of the proportion se0 = sqrt[p^ (1-p^)/N] = sqrt[ 3.0948 x 10-4 * (1 - 3.0948 x 10-4)/ 420063 ]

= 2.7139 x 10-5

so 95% confidence interval = p^ +- Z95% se0

= 30.948 x 10-5 +- 1.96 *  2.7139 x 10-5

= (2.563 x 10-4 , 3.628 x 10-4)

= (0.02563% , 0.03628%) or (0.026% , 0.036%)

(b) Here 0.0323 is under the given 95% confidence interval so the rate of cancer is same for who doesn;t use cell phone.

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