QUESTION 2: Qatar traffic department has been installed traffic light camera sys

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QUESTION 2: Qatar traffic department has been installed traffic light camera systems to identify and ticket auto drivers who fail to stop at red traffic lights When the system senses that an automobile has entered the intersection while the traffic light was red, the cameras take a photo of the front and the back of the car, as w as record a short video of the potential violation. At a later time, a police officer looks at the photos watches the video. If the officer believes there was a traffic violation, the owner of the car is fi The traffic department annually evaluates the officer assessment of the photos. For this evaluation, and to estimate the proportion of errors made, a supervisor reviews a simple random sample of all photos taken that year and either confirms the original officer's opinion, or finds an error. In 2010, the supervisor examined 200 and ned QR 6000 of 35585 camera-recorded incidents. Of these, he disagreed with 8 of the original officers' decisions. (Assume that there is no non-sampling error). (5 points ) a) Estimate the true proportion of mistakes made by the original officers. b) Estimate the standard error of your estimate in part (a). c) Are you confident that the officers made mistakes on more than 1% of the recorded incidents? Ju your answer

Explanation / Answer

Let X = number of cases where the supervisor’s decision differed from the original officer’s decision.

Then, X ~ B(n, p), where n = sample size and p = probability that the supervisor’s decision differed from the original officer’s decision, which is also equal to the proportion of cases where the supervisor’s decision differed from the original officer’s decision in the population.

Part (a)

Estimate of the true proportion of original officer’s error = sample proportion,

pcap = X/n = 8/200 = 0.04 ANSWER

Part (b)

Standard Error of estimate of the true proportion of original officer’s error

= sqrt{ pcap(1 - pcap)/n}

= sqrt(0.04 x 0.96/200)

= sqrt(0.000192)

= 0.0139.

Thus, standard error = 0.0139 ANSWER

Part (c)

This part will be answered employing the confidence interval for the population proportion, which is given by:

95% Confidence Interval for p = pcap ± 1.96[sqrt{ pcap(1 - pcap)/n}], where 1.96 = upper 2.5% point of N(0, 1).

= 0.04 ± 0.0272

= (0.0128, 0.0672)

i.e., 1.28% - 6.72% which is beyond (larger than) 1% implying that we can be 95% confident that officers made mistakes in more than 1% cases. ANSWER

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