Author Archives: hangtime

Means of Independent Samples-Sigmas Unknown & Assumed Unequal (Student t-Test)

This video covers hypothesis tests of the means of two samples where you make no assumptions at all - all you have to work with are the means and standard deviations of your samples. This is what happens in real life when you're analyzing data, so this is the one that's most important for you to know for tests and future math classes. Student t-distribution, here we come! Also included: doing these on your calculator.

This video appears on the page: Hypothesis Tests Comparing Two Means

Comparing Means When You Know Sigmas of the Populations

This video covers the type of problem where you're testing a hypothesis about the means of two samples when somehow you magically know the two samples' population standard deviations. This is not a very realistic scenario, because if you don't know the populations' means how would you know their standard deviations, but most classes cover it anyways as a way to introduce hypothesis testing of means. Also included: doing these on your calculator.

This video appears on the page: Hypothesis Tests Comparing Two Means

Overview of Mean Comparison Formulas (lots of Student t-Tests)

Hypothesis testing of two sample means is so confusing because there are four sets of formulas! This video just gives you an overview of how to approach these problems: paired (dependent) samples, samples where you know sigmas, samples where you don't know sigmas but assume they're equal, and samples where you don't know sigmas nor assume they're equal.

This video appears on the page: Hypothesis Tests Comparing Two Means

Hypothesis Tests Comparing Two Means
Overview of Mean Comparison Formulas (lots of Student t-Tests)
Comparing Means When You Know Sigmas of the Populations
Means of Independent Samples-Sigmas Unknown & Assumed Unequal (Student t-Test)
Means of Independent Samples-Sigmas Unknown But Assumed Equal (Pooled Variance)
Comparing Sample Means with Matched Pairs (Dependent)
Confidence Intervals Comparing Means of Two Samples
Mean Comparisons On Your Calculator

Testing hypotheses comparing the means of two samples (usually with a Student t-Test). Sounds simple enough, but this topic takes up a lot of space in your book because there are different formulas for each specific situation: two samples where the corresponding population standard deviations are known; two samples where the population standard deviations unknown but assumed equal; population standard deviations unknown and assumed unequal; and paired data (dependent samples). Lots of stuff to cover!

Part of the course(s): Statistics

Testing Claims About Standard Deviation
(using Chi-Square)

This video explains the least-common type of hypothesis test: testing claims about the standard deviation of a sample relative to the standard deviation of the population. Since you've already done so many hypothesis test problems about proportions and means, this is a relatively plug-and-chug affair.

This video appears on the page: Testing Claims About Standard Deviation

Testing Claims About Standard Deviation

This chapter explains the least-common type of hypothesis test: comparing the standard deviation of a sample to the standard deviation of the population using a Chi-Square test. Since you've already done so many hypothesis test problems about proportions and means, this is a relatively plug-and-chug affair.

Part of the course(s): Testing Claims About Standard Deviation ,Statistics

Hypothesis Testing Claims About Means:
P-values, critical t-values,
t-value critical values, on your calculator

This chapter contains videos covering each of the three different ways that your teacher may want you to know how to test hypotheses involving sample means: P-values, critical t-values (Student t-Test), or plugging-and-chugging on your calculator. A video also covers how to get a critical t-value from the t-table when you're not allowed to use a calculator.

Part of the course(s): Statistics

Hypothesis Testing Claims About Means Using Calculator P-value

This is the easiest method to test a hypothesis about a mean: just go into the stats menu on your calculator, select the one-sample mean test, and enter numbers directly from the word problem. You'll still have to know what a P-value and t-value mean, since that's what the calculator spits out, but at least you won't have to memorize any formulas!

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Testing Claims About Means Using Critical t-Value (Student t-Test)

This is the "other way" to test a hypothesis about a mean: most of the steps of the process are the same as using the P-value method, except instead of converting the t-value of your sample to a P-value (probability), you instead compare it to the cutoff critical t-value that you either get from your calculator or a table.

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Using t-value Table To Test P-Values (Student t-Test)

When you want to test a hypothesis using the critical t-value method, you have to first come up with the critical t-value for your given level of confidence. That's pretty easy with a calculator using the inverseT function. But if you have one of those retro professors who makes you use the table, this video explains how to do it.

This video appears on the page: Hypothesis Testing Claims About Means

Testing Claims About Means Using Critical Z-Values

This is the most common way for professors to want you to deal with hypothesis testing of sample means. It's not as easy as just using the 1-sample mean test on your calculator -- which is pure plug-and-chug -- but it's favored by teachers because it's a nice compromise between the retro method of t-tables and the no-thinking world of letting the calculator do everything for you.

This video appears on the page: Hypothesis Testing Claims About Means

Testing Claims About Proportions on Calculator

This is the easiest method to test a hypothesis about a proportion: just go into the stats menu on your calculator, select the one-sample proportion test, and enter numbers directly from the word problem. You'll still have to know what a P-value and z-value mean, since that's what the calculator spits out, but at least you won't have to memorize any formulas!

This video appears on the page: Testing Claims About Proportions

Testing Claims About Proportions Using Critical Z-Values

This is the "other way" to test a hypothesis about a proportion: most of the steps of the process are the same as using the P-value method, except instead of converting the z-value of your sample to a P-value (probability), you instead compare it to the cutoff critical z-value for the desired level of confidence.

This video appears on the page: Testing Claims About Proportions

Testing Claims About Proportions Using P-Values

This is the most common way for professors to want you to deal with hypothesis testing of proportions. It's not as easy as just using the 1-sample proportion test on your calculator -- which is pure plug-and-chug -- but it's favored by teachers because it's a nice compromise between the retro method of z-tables and the no-thinking world of letting the calculator do everything for you.

This video appears on the page: Testing Claims About Proportions

Testing Claims (Hypotheses) About Proportions:
Testing Claims About Proportions Using P-Values
Testing Claims About Proportions Using Critical Z-Values
Testing Claims About Proportions on Calculator

"Testing claims" is just another way of saying "hypothesis testing". This chapter contains three videos, one each for the three different ways that your teacher may want you to know how to do these problems: P-values, critical z-values, or plugging-and-chugging on your calculator.

Part of the course(s): Statistics

Power Of A Test (5 of 5)

This video is the first in a series explaining the basics of hypothesis testing. The power of a test -- often known as "powering a test" -- is the basic idea that if you want better data, you need larger samples. But getting larger samples is either more work, more expensive, or both, especially if you already collected data which turned out to be inconclusive. So you need to figure out ahead of time how big a sample to collect, and that is the crux of powering your test: how big to make your sample so that you won't come up short.

This video appears on the page: Hypothesis Testing Explained

Type 1 & Type 2 Errors (4 of 5)

This video is the fourth in a series explaining the basics of hypothesis testing. In it I explain what Type I and Type II errors are. I also give you the "routine for fun" memory trick for keeping the two types straight, as well as how to use this "trick", which is one of the hardest-to-use memory shortcuts I've ever seen. As always, I'll try to make it plug-and-chug for you!

This video appears on the page: Hypothesis Testing Explained

One-Tailed vs Two-Tailed Tests (3 of 5)

This video is the third in a series explaining the basics of hypothesis testing. In it I explain what 1-tailed and 2-tailed tests are, and how it affects your calculations of critical values and confidence levels.

This video appears on the page: Hypothesis Testing Explained

Null & Alternative Hypothesis (H0 & Ha)
(video 2 of 5)

This video is the second in a series explaining the basics of hypothesis testing. In this particular video, we get practice doing the first step of all hypothesis test problems: writing down the null and alternative hypotheses (H0 & Ha). I don't even do any calculations; this video is strictly about making hypothesis writing a plug-and-chug affair.

This video appears on the page: Hypothesis Testing Explained

The Logic of Hypothesis Testing (1 of 5)

This video is the first in a series explaining the basics of hypothesis testing. It will help you understand the basic concept behind every hypothesis test questions, which is always this: They give you some data that APPEARS to show some effect (a new medicine is better than the old one, the coin is weighted towards heads, things are different than in the past, etc.). But what if the effect is due to random luck (a.k.a. sampling error) as opposed to the effect being real? Well, you calculate the odds of it being due to luck, and if that's a low probability, you assume the effect must be real.

This video appears on the page: Hypothesis Testing Explained