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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 - )) / n)

= 2.576 (((0.290 * 0.710) / 62)

= 0.148

A 95% confidence interval for population proportion p is ,

± E   

= 0.290  ± 0.148

= ( 0.142, 0.438 )

orchestra answered 2 years ago
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