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In: Statistics and Probability

A survey of 500 non-fatal accidents showed that 201 involved the use of a cell phone....

A survey of 500 non-fatal accidents showed that 201 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.

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SOLUTION:

From given data,

A survey of 500 non-fatal accidents showed that 201 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.

= 201

= 500

= /  

= 201 / 500

= 0.402

q = 1 -

= 1 - 0.402

= 0.598

99% confidence interval

Confidence interval is 99%

99% = 99/100 = 0.99

= 1 - Confidence interval = 1-0.99 = 0.01

/2 = 0.01 / 2

= 0.005

Z/2 = Z0.005  = 2.576

Margin of error

E = Z/2 *

E = 2.576  *

E = 2.576  * 0.021926969​​​​​​​

E = 0.0564838​​​​​​​

At 99% Confidence interval   is

- E <  P <  + E

0.402 - 0.0564838​​​​​​​ <  P <  0.402+ 0.0564838​​​​​​​

0.3455 <  P <  0.4584

orchestra answered 2 years ago
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