Question

In: Statistics and Probability

A study of 420,026 cell phone users found that 138 of them developed cancer of the...

A study of 420,026 cell phone users found that 138 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 0.0411% for those not using cell phones. The data are from the Journal of the National Cancer Institute.

a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

Expert Solution

SOLUTION:

From given data,

A study of 420,026 cell phone users found that 138 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 0.0411% for those not using cell phones. The data are from the Journal of the National Cancer Institute.

Where,

x = 138

n = 420026

p = x/n = 138/420026 = 0.000328

q = 1-p = 1-0.000328 = 0.999672

a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

95% confidence interval

Confidence interval is 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = Z_/2 * sqrt(p(1-p) / n)

Margin of error = 1.96 * sqrt(0.000328(1-0.000328) / 420026 ) = 0.0000547

95% C.I

Lower limit = p - Margin of error = 0.000328 - 0.0000547 = 0.00027 = 0.027 %

Upper limit = p + Margin of error = 0.000328 +0.0000547 = 0.00038 = 0.038 %

orchestra answered 2 years ago

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