Author Archives: hangtime
Confidence Intervals For Variance & Standard Deviation
This is the type of confidence interval problem where they give you some info about a sample, like its standard deviation, and then you use the Chi-Square Distribution and a couple of formulas to spit out a confidence interval estimate of the standard deviation of the population the sample was taken from.
This chapter covers the type of confidence interval problem where they give you some info about a sample, like its standard deviation, and then you use the Chi-Square Distribution and a couple of formulas to spit out a confidence interval estimate of the standard deviation of the population the sample was taken from.
Chi-Square Critical Values
Like all the other distributions you use in stats, with Chi-Square you frequently have to turn to a table and look up the "critical values" for the problem you're working on, which basically means finding the value of Chi-Square which creates a "tail" with an area of .005 or .05 or whatever level of confidence you're working with.
The Chi-Square Distribution
This video introduces a few aspects of the Chi-Square distribution that you're supposed to know off the top of your head, either for the test or because it will help you get what's going on with the problems that use this funky distribution.
Minimum Sample Size for Proportion Estimates
As you know, bigger samples lead to smaller margins of error. This video covers the type of problem where they give you the margin of error, then ask you to calculate the minimum sample size you'd have to take in order to accomplish that margin of error.
Confidence Intervals For Proportions
This video covers problems where you are given a proportion or percentage of a sample which has come quality (p), and you are asked to estimate a confidence interval for the population proportion with that same characteristic. Since you're working with p and q, as usual this only works for larger sample sizes.
These videos cover problems where you are given a proportion or percentage of a sample which has come quality (p), and you are asked to estimate a confidence interval for the population proportion with that same characteristic.
This chapter covers the basics of the Chi-Square Distribution (X2). Chi-Square gets a lot of play throughout stats, so this chapter just covers the basics of the distribution, its properties, the (X2)table and what happens for larger degrees of freedom.
Confidence Intervals of Means -- Sigma NOT Known
This video covers the type of confidence interval problem where they give you the stats of the sample -- mean and standard deviation -- but you do NOT know sigma (standard deviation of the population), so you have to use the Student t-distribution to calculate your margin of error and confidence interval.
This chapter covers the type of confidence interval problem where they give you the stats of the sample -- mean and standard deviation -- but you do not know sigma (standard deviation of the population), so you have to use the Student t-distribution to calculate your margin of error and confidence interval.
t-Values On Your Calculator
Just like with z-values, your calculator has a few different functions that can replace looking up values in a table. But these ones don't quite do the work for you the way the normal distribution functions do.
Student t-Distribution Table
This video explains how to look up critical t-values on the t-distribution table. You'd think it would be crazy because the numbers are all different depending on degrees of freedom (df), but unlike z-values, the t-value table only covers the most common values you would need for various levels of confidence -- 90%, 95%, 99%, etc -- so it ends up being pretty manageable.
Student t-Distribution
This video explains a few of the things you're supposed to know about the Student t-Distribution, including the strange fact that it has a different shape depending on your sample size (a.k.a. "degrees of freedom", a.k.a. "df").
This chapter introduces "Student's t-Distribution", which is kind of like the normal distribution, except it's got t-values instead of z-values. You'll be using t-values tons from here on out, for lots of different types of Student t-Tests, where you use t instead of z for smaller sample sizes and when you don't know the population standard deviation (i.e. real world applications).
Minimum Sample Size When Sigma Is Known
This video covers a particular type of confidence interval problem where instead of giving you a sample size and asking for the confidence interval, they give you the intended margin of error and ask you to calculate the minimum sample size to attain that level of precision. This video's formulas only work when you know POPULATION standard deviation (not just for sample).
Confidence Intervals When Sigma Is Known
This video works a bunch of examples of how to plug-and-chug your way through confidence interval and margin of error problems where you are told the POPULATION standard deviation (sigma), yet somehow you can only estimate the population mean using the mean of a sample. Pretty contrived, but every prof uses these to introduce the concepts of confidence intervals.
The next few chapters each cover a specific type of confidence interval problem. This chapter covers the first type that most books cover, the ones where they tell you the mean of a sample but sigma FOR THE ENTIRE POPULATION and ask you to calculate a confidence interval to estimate the mean of the population. How, you may ask, would you know the standard deviation of an entire population but not the mean? Exactly. These are just a non-realistic type of problems that books use to introduce the concept of confidence intervals.
Critical Z-Values In Confidence Intervals
This video introduces the concept of a critical value, and then goes through some of the most common ones that you'll see again and again in confidence interval problems: z-values for 90%, 95%, and 99% confidence intervals.
What A Confidence Interval Does NOT Tell You
I normally steer clear of mathy topics, but this one seems to get hit by every teacher and book, so it's worth taking on. Specifically, what words are you allowed to use when describing confidence intervals, and what words will get you busted down to private.