In an attempt to slow down traffic, police installed a stationary radar gun with

Question

In an attempt to slow down traffic, police installed a stationary radar gun with a sign that displays the speed of cars approaching it. Prior to placing the sign, police randomly selected 100 cars passing that position and recorded 65 cars in excess of the posted speed limit. After placing the sign, police randomly selected 100 cars passing the same position and recorded 55 cars in excess of the posted speed limit (a) Frequentist analysis i. Calculate an approximate pvalue for the hypothesis test with alternative hypothesis that the true population proportion decreased after the sign was posted ii. Calculate an approximate 90% confidence interval for the decrease in true population propor- tion after the sign was posted (b) Bayesian analysis using the default prior. i. Calculate an approximate posterior probability that the true population proportion decreased after the sign was posted ii. Calculate an approximate 90% credible interval for the decrease in true population proportion after the sign was posted (c) Do you think the true population proportion was lower after the sign was placed? Why or why not? In addition to recording the number of cars in excess of the speed limit the police also recorded the speed of those cars. The following is a summary of the data: d

Explanation / Answer

In an attempt to slow down traffic, police installed a stationary radar gun with a sign that displays the speed of cars approaching it. Prior to placing the sign, police randomly selected 100 cars passing that position and recorded 65 cars in excess of the posted speed limit. After placing the sign, police randomly selected 100 cars passing the same position and recorded 55 cars in excess of the posted speed limit (a) Frequentist analysis i. Calculate an approximate pvalue for the hypothesis test with alternative hypothesis that the true population proportion decreased after the sign was posted ii. Calculate an approximate 90% confidence interval for the decrease in true population propor- tion after the sign was posted (b) Bayesian analysis using the default prior. i. Calculate an approximate posterior probability that the true population proportion decreased after the sign was posted ii. Calculate an approximate 90% credible interval for the decrease in true population proportion after the sign was posted (c) Do you think the true population proportion was lower after the sign was placed? Why or why not? In addition to recording the number of cars in excess of the speed limit the police also recorded the speed of those cars. The following is a summary of the data: d

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