Problem 8 Traffic Stops and Traffic Tickets Stopped by Traffic Cop Ticket Just a
ID: 3306644 • Letter: P
Question
Problem 8 Traffic Stops and Traffic Tickets Stopped by Traffic Cop Ticket Just a Issued | warning | Total | 11 | 15 | 97 | 89% 70 | 7996 Men 86 Women 55 One of my friends- call him Maurice -had several traffic tickets, and he knew one more would trigger a suspension. He felt that women stopped by a traffic cop were more likely than men to get off with just a warning, and for his Field Project he set out to prove it, with = 0.05. Maurice quickly realized that he should test whether men and women stopped by a cop are equally likely to get a ticket, not just whether men are more likely. After all, he couldn't rule out the possibility that women are more likely to get a ticket if stopped. Maurice distributed a questionnaire to a systematic sample of Manhattan College students. He assumed that any gender-based difference the students would be representative of college students in general. That seems reasonable.) He asked three questions: 1. Male or female? 2. Stopped by a traffic cop since your 18th birthday? 3. If yes, did you receive a ticket the last time you were stopped? Maurice disregarded any questionnaires from students who had never been stopped as adults. He wasn't interested in the likelihood of getting a ticket, but in the likelihood of getting a ticket after being stopped by a cop. Analyze this problem.Explanation / Answer
Here the research problem of maurice is that after being stopped by a cop, males have more chances to get a parking ticket than the females".
He sets two hypothesis for that
Null HYpotheiss : H0 : There is no difference in proportion of males who got parking ticket after being stopped by a cop than females who got parking ticket after being stopped by a cop. pfemale = pmale
ALternative Hypothesis : Ha : Proportion of males who got parking ticket after being stopped be a cop is statisticaly more than proportion of females who got parking ticket after being stopped by a cop. pmale > pfemale
so sample proportion of such male after survey p^male = 0.89
sample proportion of such female after survey p^female = 0.79
Pooled estimate = (Total ticket issues)/ Total people stopped (p)= (86 + 55)/ (97 + 70) = 0.8443
Standard error of the proportion of difference se0 = sqrt [p * (1-p) * (1/n1 + 1/n2 )]
= sqrt [ 0.8443 * 0.1557 * (1/97 + 1/70)] = 0.057
Test statistic
Z = (p^male - p^female )/ se0 = (0.89 - 0.79)/ 0.057 = 1.754
as the given test is one sided so Zcritical = 1.645 for alpha = 0.05
so here test statistic Z > Zcritical so we shall reject the null hypothesis and can conclude that Proportion of males who got parking ticket after being stopped be a cop is statisticaly more than proportion of females who got parking ticket after being stopped by a cop. So, maurice is true in this respect.