Author Archives: hangtime

What Is A Confidence Interval?

This video gets the confidence ball rolling by explaining in normal English what the point of these crazy things is (hint: if you're majoring in anything besides math or physics, this is the most useful thing you've done in stats thus far). Also covered are the concept of margin of error, and how to spot a confidence interval problem.

This video appears on the page: Intro to Confidence Intervals

Intro to Confidence Intervals:
What Is A Confidence Interval?
What A Confidence Interval Does NOT Tell You
Critical Z-Values In Confidence Intervals

This chapter introduces the concept of confidence intervals, along with the most important concepts you're supposed to understand for multiple choice type questions. Also very importantly, it explains the definition of confidence intervals -- and what they are NOT -- because for some reason every Stats teacher and book seems to make a really big deal about the exact words you use to describe what a confidence interval tells you. Sticklers!

Part of the course(s): Statistics

Normal Approximation of Binomial Distributions

Not all classes cover this topic. The basic idea is that some binomial distribution problems -- for example, finding the probability that if you flip a coin 8 times you'll get 5 or more heads -- get really time-consuming for larger numbers of flips (trials). It's the "or more" that gets you. Using z-values makes this type of problem a lot faster and easier!

Part of the course(s): Statistics

Normal Approximation of Binomial Distributions

The basic idea is that some binomial distribution problems -- for example, finding the probability that if you flip a coin 8 times you'll get 5 or more heads -- get really time-consuming for larger numbers of flips (trials). It's the "or more" that gets you. Using z-values makes this type of problem a lot faster and easier!

This video appears on the page: Normal Approximation of Binomial Distributions

Central Limit Problems Using Sample Proportions

This video covers word problems requiring the sample proportions versions of the Central Limit Theorem formulas. These problems always start by giving you the percentage of a population that has a certain characteristic, then ask you the probability that the proportion of a random sample will be either greater or less than that of population at large. Z-values and calculator, hear we come!

This video appears on the page: Sampling Means & Sampling Proportions Example

Central Limit Problems Using Sample Means

This video covers how to do Central Limit Problems which require the sampling mean approach. These are the problems that give you the mean and standard deviation of some population, then ask you the probability that the mean of a random sample will be either more or less than that. Z-values and calculator, hear we come!

This video appears on the page: Sampling Means & Sampling Proportions Example

Sample Mean vs Sample Proportion: When To Use Which

This video teaches you to spot which Central Limit Theorem problems should be approached using sample means and the related formulas, versus which problems require the sample proportions approach.

This video appears on the page: Sampling Means & Sampling Proportions Example

Central Limit Theorem Examples:
Sampling Means & Sampling Proportions
Sample Mean vs Sample Proportion: When To Use Which
Central Limit Problems Using Sample Means
Central Limit Problems Using Sample Proportions

In the previous chapter we took a look at the Central Limit Theorem from a more theoretical viewpoint, looking at distrubutions of p-hats and x-bars. Now we'll get into doing lots of examples of the two types of word problems that use the CLT: they give you a population's mean and standard deviation or proportion, then ask you the probability that a random sample would have a certain average or proportion.

Part of the course(s): Statistics

Rules for Central Limit Theorem

This short video explains the "criteria" for when you're allowed to use the central limit theorem. Not that you'd care, except that's often the first step of test and AP questions.

This video appears on the page: Central Limit Theorem

Intro to Central Limit Theorem

This video explains what the central limit is, and outlines how you'll be using it to solve big fancy word problems. It also shows you where that graph comes from that's in every book and lecture on the topic: a pile of sample variances, x-bars and p-hats stacked up in the shape of a normal distribution.

This video appears on the page: Central Limit Theorem

Central Limit Theorem
Intro to Central Limit Theorem
Rules for Central Limit Theorem

This chapter tells you what the central limit theorem says, shows you how to draw those little distributions with all the x-bars and p-hats piled up into normal distributions, and explains the rules to when you're allowed to use this thing. The problems you can do with this thing come in the next chapter.

Part of the course(s): Statistics

Finite Population Adjustment for Standard Error

Usually when you're working with sampling distributions, you assume that the population (N) is very large compared to the sample size (n). But sometimes you'll see problems where they tell you the population size, and it's small, so keep an eye out because you'll need to "adjust" the standard error with the formula in the thumbnail.

This video appears on the page: Sampling Distributions—xbar, phat

Standard Error

This is that symbol that looks like it should be called the "standard deviation of the distribution of sample means which you use to find the z-value of a sample mean relative to its sampling distribution of the means." Maybe "standard error" was just shorter?

This video appears on the page: Sampling Distributions—xbar, phat

Sampling Distribution Vocab

This video goes through all the symbols you can see in the thumbnail to the right -- phat (pronounced pee-hat), standard error, etc -- explaining what they mean and also what they're called, to help you figure out what terms to look for to find more videos about each one.

This video appears on the page: Sampling Distributions—xbar, phat

Sampling Distribution vs Sample Distribution

This video explains what a sampling distribution is (distribution of sample means and variances), how it's different from a sample distribution (without the -ing), and gives you a taste of what the central limit theorem is going to be all about.

This video appears on the page: Sampling Distributions—xbar, phat

Sampling Distributions (x-bar, p-hat),
Distribution Of The Sample Mean:
Sampling Distribution vs Sample Distribution
Sampling Distribution Vocab
Standard Error
Finite Population Adjustment for Standard Error

These videos cover sampling distributions of the mean and proportion, also known as the "distribution of the sample mean" and "distribution of the sample proportion." Lots of examples and vocab, including p-hat (phat), so that you'll be ready for the central limit theorem.

Part of the course(s): Statistics

Exponential Probability Distributions (Continuous)

This chapter covers a type of distribution that many classes don't cover -- exponential distributions -- which tells you the chances of an event happening in the immediate future. For example, if someone walks into Starbucks every 2 minutes on average, what are chances of someone walking in within the next 1 minute.

Part of the course(s): Statistics

Exponential Probability Distributions (Continuous)

This video covers a type of distribution that many classes don't cover -- exponential distributions -- which tells you the chances of an event happening in the immediate future. For example, if someone walks into Starbucks every 2 minutes on average, what are chances of someone walking in within the next 1 minute.

This video appears on the page: Exponential Probability Distributions (Continuous)

Z-Score Table Calculations On Your Calculator

This video covers how to use your calculator to replace the z-score table that's in your book. If you don't get to use a calculator on the test, that's obviously not going to help you, but many z-table problems can be done just on your TI-84.

This video appears on the page: Calculating Probability Using Z-Score & Normal Distribution

How To Use Z-Score Table To Calculate Probability & Proportion

Now that we've covered the basics of this type of problem in the preceding videos, we're finally ready for 30 minutes of awesome examples which will make you the master of transforming x's to z's and back again!

This video appears on the page: Calculating Probability Using Z-Score & Normal Distribution