Question

The city mayor wants to know how long it takes the police in his city to respond to crime. In a random sample of 20 citizens who called the police for service, the mayor’s special adviser on crime found that the average response time was 560 seconds, with a standard deviation of 45 seconds. Construct a confidence interval around your point of estimate and tell the mayor the police response time.

Answer 1

We are not given the confidence level here for the confidence interval. Let us compute the 95% confidence interval here for the time taken for the police in his city to respond to crime. For n - 1 = 19 degrees of freedom, we get from the t distribution tables:

P( -2.093 < t₁₉ < 2.093) = 0.95

Therefore the confidence interval here is obtained as:

X +

45 560 +2.093 * *20

560 + 21.0604

(538.9396.581.0604)

This is the required 95% confidence interval here. The interpretation of this is that the mean time time taken for the police in his city to respond to crime lies in the above interval with 95% confidence level.