# Bloomington Tutors | Blog Finite math, K201, calculus, and statistics explained

Statistics
Apr 08, 2015

## When to use the z-test versus t-test

How do I know when to use the t-test instead of the z-test?

Just about every statistics student I've ever tutored has asked me this question at some point. When I first started tutoring I'd explain that it depends on the problem, and start rambling on about the central limit theorem until their eyes glazed over. Then I realized, it's easier to understand if I just make a flowchart. So, here it is!

Basically, it depends on four things:

1. Whether we are working with a mean (for example, "37 students") or a proportion (e.g., "15% of all students").
2. Whether or not we know the population standard deviation ($\sigma$). In real life we usually don't, but statistics courses like to contrive problems where we do.
3. Whether or not the population is normally distributed. This is mainly important when dealing with small sample sizes.
4. The size of our sample. The magic number is usually 30 - below that is considered a "small" sample, and 30 or above is consi...

Finite M118
Aug 24, 2014

## Practice for your finite exams with our sample problems!

Welcome, new and returning IU students! I hope everyone had a great summer and is ready (sorta?) to get back to class. Here at Bloomington Tutors, we've been working hard all summer and getting ready to help you succeed.

We've launched our practice exam system for finite math (M118), and hope to start adding materials for calculus and other courses soon as well. Check out our finite questions here: https://bloomingtontutors.com/quiz/finite-math

They're interactive multiple-choice questions, with explanations for the wrong answers (i.e., we try to guess the common mistakes you might have made to get that answer, and offer you an explanation).

Enjoy!

Finite M118
Oct 30, 2013

## A linear programming word problem - with a surprise twist!

Today, I thought I'd tackle a problem from one of the most "popular" courses (read "required for almost all majors") at this school - finite math. For those of you who haven't heard of this course before, finite math is actually an amalgam of miscellaneous topics from probability theory, linear algebra, and stats, created by math departments at various universities as a way to introduce college freshmen to rigorous, analytical thinking. It's not a real field of mathematics, in the sense that you won't find any professional mathematicians who specialize in "finite mathematics." However, there are mathematicians who specialize in the topics introduced in this course, such as combinatorics and probability.

One of the topics covered in finite math ("finite", by those in the know) is linear programming. This is basically a fancy term for a constrained optimization problem consisting of linear constraints and a linear objective function. In this blog post, I will tackle the followin...

Calculus M119
Apr 06, 2013

## An easier way to take the derivative of complicated logarithmic functions

Math can often feel overwhelming. Sometimes, it just looks overwhelming, even when you actually know how to do it. This visual intimidation factor is something that breeds anxiety, induces brain farts on tests, and ultimately turns a lot of people off to math. Case in point, our calculus problem this evening:

Example: Find the first derivative of:

$f(x)=ln\left (\frac{(3x-7)^{4}(x+1)^{2}e^{2x}}{ln(x)\sqrt{2x^2-x}} \right )$

Hint: There is an easy way, and a hard way to approach this problem. Use the easy way.

This function, frankly, looks terrifying. Its full of exponents and natural logs and square roots, all jammed up against one another in some night-before-the-test anxiety dream. The hint provides a glimpse of comfort, if only we can figure out the "easy way." If not, we'll be doing chain rules inside product rules inside quotient rules inside chain rules all night, run out of time, and probably fail the exam. Basically, if you see a problem...