Question
In: Statistics and Probability
18 students got a speeding ticket last year while 44 did not. Find a 99% CI...
18 students got a speeding ticket last year while 44 did not. Find a 99% CI for the population proportion of students that received a speeding ticket last year.
Solutions
Expert Solution
Solution :
Given that,
n = 18 + 44 = 62
x = 18
Point estimate = sample proportion = 
= x / n = 18 / 62 = 0.290
1 -
= 1 - 0.290 = 0.710
At 99% confidence level
= 1 - 99%
=1 - 0.99 =0.01
/2
= 0.005
Z/2
= Z0.005 = 2.576
Margin of error = E = Z
/ 2 * ((
* (1 -
))
= 2.576 (
= 0.148
A 95% confidence interval for population proportion p is ,
± E
= 0.290 ± 0.148
= ( 0.142, 0.438 )
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