Subject Mathematics General Statistics


Problem 1.
You operate a 311 Clearinghouse for the City of Autopia. The City’s 311 system, which supports reporting of city problems, has been in place since 2000, but received heightened attention in 2010, when newly elected Mayor Michael Bluth implemented a “Rapid Response” system for potholes, graffiti, and parks. Under his Rapid Response system, the Mayor increased advertising of the 311 system, and added staff to the 311 dispatch system.
In 2012, the city adopted a new 311App that allows residents to use social media (Twitter and Facebook) to notify the City of problems in these areas. Subsequently, the City has been receiving negative press that it has been dragging its feet in responding to complaints. The Mayor has asked you to provide performance statistics to response to these charges and demonstrate the success of the Rapid Response Initiative and the 311App.
The process for handling 311 complaints is shown in Figure 1, below. The city’s PerformanceStat system records the date that the 311 request is received, date of dispatch; date that service is scheduled, and date that service is completed.

311 dispatch team confirms presence of problem and sends request to responsible department -> Service department processes 311 request and schedules service -> Service completed

Worksheet #1 summarizes PerformanceStat data on the number of complaints in each category (potholes, graffiti, and parks) for the period of 2000 to 2014. In addition, for a sample of 50 service complaints of each type in 2014, it summarizes data on the time required to complete the 311 process. The data are processing days by service type for each of the “signposts” in the rapid response process (dispatch, service repair scheduled to begin, and completion of service).

A. Produce a line chart that displays time trends for the number of complaints by service category. On the chart, indicate the initiation of the Rapid Response system and implementation of the 311 App. Ignoring statistical significance, what visual scrutiny of the chart suggest about possible effects of the Mayor’s initiatives? How might you explain the relative differences between reporting trends by type of service (hint: in Autopia, most graffiti is found in very low income areas of the city, areas that are also unfortunately underserved by parks).

B. For each of the three service areas, calculate the mean and standard deviation of the days that it takes to process a 311 complaint through each “signpost.” (IE: days to dispatch; scheduled repair; completion of repair).

C. Create a bar chart that displays the average time to completion for each step by service type.

D. Which step(s) are taking the longest, and how do patterns differ across services? Which steps and/or services experience the greatest degree of variability?

E. Considering this information, discuss what you might consider doing to improve the responsiveness of the 311 system.

Problem 2.   
You have been retained by a school district to conduct the evaluation required by a foundation grant it received to increase college readiness among at-risk teenagers. In each of the district’s three high schools, the grant paid for a counselor trained to identify at risk youth at the end of sophomore year and to provide counseling support during junior year to help them identify their life goals, seek curricular support, and prepare for college. College readiness was measured by a survey that was administered at the beginning and end of the counseling sessions. Worksheet #2 in the Excel workbook provides data on the results for 20 youth who participated in the program in each of the three high schools. The variable “hours” is the number of hours of counseling received by the youth. The variable “Difference” is a record of the change in score that the youth received on the college instrument.

A. Calculate the mean and standard deviation for each variable.

B. Calculate the correlation between hours and difference score for each of the four schools.   Also test whether these correlations are significantly different from zero. You may simplify this task by calculating the p-value at the website linked below.   Interpret what the correlations and associated p-values tell you about the program.

C. Based on these results do you think that there are important differences in the efficacy of the three high school counseling programs?

D. Draw scatter plots that present the relationship between hours and difference scores for each of the 3 schools.   

E. What do you observe about the pattern of results at each school? What do these results suggest about the relationship between increased counseling hours and test scores within each school?

F. What issues with internal validity do you identify with this evaluation design? What would you recommend to improve the design for the remaining two years of the foundation grant?

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Descriptive Statistics and Correlation

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