# Big Assignment: Due before the last day of class, Wednesday May 31. 

Imagine that you are "Statistical Services" and that you have received the below request for you services. ÊYour assignment is:

1. ÊHelp Dr. Blanchette to answer the questions posed the below letter.  You are to attempt this given only the information contained in this letter.

2.  Prepare a list of requests for more information about this experiment and/or the experiment's goals that would help you to better analyze the data.  For each request, you should describe how this information might change you interpretations of the data and/or improve your analysis.  (In chapters 11-13 many issues are discussed which might apply. You should make  at least one such request in order to pass this assignment.)

3.  Address the letter's postscript.  Namely, you must make at least one suggestion about the protocol and/or design of a possible future version of this experiment. 

###### The letter:

Dear Statistical Services,

We collected some data in order to help us understand how people perceive age in our culture.

What we did: I asked my graduate student Theodore Smith to find 20
people here in Berkeley between the ages of 20 and 80 that were willing to be a part of our experiment and have their picture taken.  I will call them our Subjects. I asked Theodore to try to make sure that the ages of our Subjects were relatively spread out. Theodore found 20 such Subjects (labeled 1 though 20 in the data set PictData2.txt) and I was happy with our subjects age distribution, so we used these initial 20 Subjects. ÊHe asked each of our Subjects for their age (the column A2), their gender (Column G2 with 1=Female, 2=Male), and their race (Column R2 with 1=White, 2=Black or African American, 3=Hispanic or Latino, 4=Asian, 5=Native American.)

With the photos of our Subjects, we performed the following experiment. ÊWe randomly selected 5 US cities, took a trip to each city, and while attempted to randomly select 200 people to take our "quiz" of guessing the ages our 20 Subjects form their photographs. ÊIt turned out to be a more time consuming process than we had anticipated, and we only ended up collecting 890 total responses.  We called the 890 people who took our "quiz" our Samples. We collected the responses from our Samples the Data set Data2.txt. ÊIn this files, each row represents one of our Samples while the columns correspond to their ages (column A1), their genders (Column G1 with 1=Female, 2=Male), their races (Column R1 with 1=White, 2=Black or African American, 3=Hispanic or Latino, 4=Asian, 5=Native American, 7=Other), and each Samples Estimate of the ith Subject's age (Column Ei).

Our statistical ideas have not been working well, so rather than
prejudice you with what we have already attempted, we will simply see if you can use this data to help us answer the following questions: 

How well can people estimate other people's ages?

Is the ability to correctly estimate an person's age dependent onÊrace, gender, and/or age (of a Subject and/or of a Sample)? If so, then can we describe these dependencies?

Can we form a predictive model that would allow us to take race, gender, and age data and then predict what age a new Sample is likely to estimate as the age of a new Subject?

Thank You,

Dr. Blanchette

P.S: We have funding to run a second such experiment, and any advice
you have concerning Êthe protocol and/or the choice of data to collect next time would be very welcome.