It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets.What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?
A)0.620

Question

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets.What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?
A)0.620 < p < 0.780
B)0.591 < p < 0.812
C)0.584 < p < 0.830
D)0.615 < p < 0.805

Quizplus · Accepted Answer

We can use the formula 
p ± z*(sqrt(p*(1-p)/n))
where p is the sample proportion (0.7), n is the sample size (90), and z* is the critical value of the standard normal distribution corresponding to a 90% confidence level (1.645). 
Plugging in these values, we get 
0.7 ± 1.645*(sqrt(0.7*(1-0.7)/90)) 
= 0.7 ± 0.08 
Therefore, the 90% confidence interval is 
0.62 < p < 0.78. 
The closest choice is A.

It Was Found That in a Sample of 90 Teenage