Question

A study of

420 comma 022420,022

cell phone users found that

133133

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

0.03270.0327​%

for those not using cell phones. Complete parts​ (a) and​ (b).

a. Use the sample data to construct a

9090​%

confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

nothing​%less than<pless than<nothing​%

​(Round to three decimal places as​ needed.)

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.

YesYes​,

because

0.03270.0327​%

isis

included in the confidence interval.

B.

NoNo​,

because

0.03270.0327​%

is notis not

included in the confidence interval.

C.

NoNo​,

because

0.03270.0327​%

isis

included in the confidence interval.

D.

YesYes​,

because

0.03270.0327​%

is notis not

included in the confidence interval.

Answer 1

Sample proportion = 133 / 420020 = 0.000317

90% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.000317 - 1.645 * sqrt(0.000317 * 0.999683 / 420022) < p < 0.000317 + 1.645 * sqrt(0.000317 * 0.999683 / 420022)

0.000272 < p < 0.000362

That is

0.027% < p < 0.036%

0.0327% lies in this confidence interval. We fail to reject the null hypothesis.

No, because 0.0327% include in the confidence interval.