Question 3 [10 marks] In a preliminary study to determine whether the installati

Question

Question 3 [10 marks] In a preliminary study to determine whether the installation of a camera designed to catch cars that goes through red lights affects the number of violators, the number of red-light runners was recorded for each day of the week before and after the camera was installed. These data are listed in table below. Can we infer that the camera reduces the number of red-light runners? 5% significance level. Day Mon Tuesday Wednesday Thursday Friday Saturday Surnday 21 Before After 27 24 18 19 20 24 16 7 16 19 17 18 Question 4 [8 marks] The length of life of a component operating in guidance control system for missiles is assumed to follow a Weibull distribution with density function

Explanation / Answer

Ho: the camera does not reduce the number of red-light runners

Ha:the camera reduces the number of red-light runners

The test statistic is

t=mean difference/std. error

=1.857/0.937

=1.98

Given a=0.05, the critical value is t(0.05, df=n-1=6) =1.94 (from student t table)

Since t=1.98 is larger than 1.94, we reject Ho.

So we can conclude that the camera reduces the number of red-light runners

19.000 mean Before 17.143 mean After 1.857 mean difference (Before - After) 2.478 std. dev. 0.937 std. error 7 n 6 df

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