In: Statistics and Probability
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.
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