The lab I have been looking at is on Parametric Curves. These are where you have two variables and a function that graphs them. But instead of using one function in terms of x and/or y:
$y=f(x)$ or $z=f(x,y)$,
parametric curves give the values for x and y as a function of t. So:
$x=x(t)$ and $y=y(t)$
This way of representing curves can be very useful with circles and polar coordinates. The questions that they ask deal mostly with parameters of $sin(at)$ and $cos(bt)$. The first few questions start exploring functions and seeing what they do with different values, how they intersect, etc. And then forming conjectures based on the data.
My name is Marc and I have an interest in randomized response which is a technique developed by Stanley Warner in 1965 that is used to obtain accurate results on surveys that ask delicate questions. For example, if you want to ask people in a classroom if they are sexually active, you can create a decoy question involving the flipping of a coin. The more delicate question can then be asked in tangent with this decoy question and nobody really knows if the participants are answering yes to the decoy question or the real question. This is done in order to make people feel more comfortable about their privacy. A program is used in this lab that simulates a randomized response survey.
One of the questions involves finding a function for a particular survey. By using a proportion concerning the number of yes answers versus the number of total answers, it is asked to find an equation that can help in estimating what the true number of yeses should be to the real question. Further questions build on determining how to uncover accurate results using the probabilities in possible answers from the real question and the decoy question.
I think this is a very useful lab for statistical analysis because you want people to be honest when gathering data but you simply cannot rely on honesty. Finding an accurate way to collect data while helping others to feel comfortable in being honest helps in gathering accurate data.