Secondary Catalogue

Mathematics

Vertex, Axis, Focus, Directrix of a Hyperbola

Analytic Geometry

Hyperbolas are conic sections that are like double parabolas. In this video we'll look at all the different geometric components of the graph of a hyperbola, including its vertex, axis, focus, and its directrix.

Test Statistics for One- And Two-Tailed Tests

Hypothesis Testing

When we run a hypothesis test, we can choose an upper-tail test, a lower-tail test, or a two-tail test, but it's really important that we make a conservative decision about the type of test we'll run. Once we pick our test type, then we'll...Show More

Confidence Interval for the Difference of Means

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two means. In this video we'll talk about how to build a confidence interval around the...Show More

Confidence Interval for the Proportion

Sampling

In this video we'll look at how to build a confidence interval around the proportion of a population. The confidence level is something that we choose based on how confident we want to be in our conclusion. Of course, it's intuitive to think that...Show More

Building Histograms from Data Sets

Visualising Data

In this video we'll work on actually building a histogram from a data set. In order to build a histogram, we'll need to determine the class interval, which means we'll need to look at class width and class midpoint.

Normal Lines

Derivatives: Tangent and Normal Lines

Learn how to find the equation of the normal line at a given point. To find the equation of the normal line, you'll need to first calculate the derivative of the function, then plug the given point into the derivative to find the slope of the...Show More

Chi-Square Tests

Regression

In this video we'll look at several examples of different types of chi-square tests, including a test for homogeneity, a test for association/independence, and a goodness-of-fit test.

Sampling Distribution of the Sample Mean

Sampling

The sampling distribution of the sample mean is created when we take every possible sample from our population, calculate the sample mean for each sample, and the plot all of those samples into a probability distribution. The SDSM is what allows...Show More

Correlation Coefficient and the Residual

Regression

In this video we'll learn how to calculate the correlation coefficient and residual for a data set, and we'll look at how these values relate to the scatterplot of the data.

Confidence Interval for the Mean

Sampling

In this video we'll look at how to build a confidence interval around the mean of a population. The confidence level is something that we choose based on how confident we want to be in our conclusion. Of course, it's intuitive to think that we...Show More

Matched-Pair Hypothesis Testing

Hypothesis Testing

Normally when we're looking at the difference of means, we're dealing with independent samples, samples that don't impact each other. But sometimes we'll want to do hypothesis testing with dependent samples. When this is the case, we can run a...Show More

Hypothesis Testing for the Difference of Means

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two means. In other words, sometimes we'll want to look at the difference between the means...Show More

Hypothesis Testing for the Difference of Proportions

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two means. In other words, sometimes we'll want to look at the difference between the...Show More

Sampling Distribution of the Sample Proportion

Sampling

The sampling distribution of the sample proportion is created when we take every possible sample from our population, calculate the sample proportion for each sample, and the plot all of those samples into a probability distribution. The SDSP is...Show More

The Student’s T-Distribution

Sampling

The student's t-distribution is another probability distribution, very similar to the normal distribution. In fact, the values we find from the t-table are often almost identicial to the values we find from the z-table. But under certain...Show More

Conditions for Inference with the SDSP

Sampling

In order to make statistical inferences using the sampling distribution of the sample proportion, we have to meet three conditions with our sample. It must be normal, large enough, and independent. In this video we'll talk about the specific...Show More

Conditions for Inference with the SDSM

Sampling

In order to make statistical inferences using the sampling distribution of the sample mean, we have to meet three conditions with our sample. It must be normal, large enough, and independent. In this video we'll talk about the specific definition...Show More

Confidence Interval for the Difference of Proportions

Hypothesis Testing

We've done hypothesis testing around point estimates, like the mean or the proportion, but now we want to work a hypothesis test around the difference of two proportions. In this video we'll talk about how to build a confidence interval around...Show More

Binomial Random Variables

Discrete Random Variables

Remember that “bi” means two, so a binomial variable is a variable that can take on exactly two values. A coin is the most obvious example of a binomial variable because flipping a coin can only result in two values: heads or tails.

Analysing Data

Range and interquartile range (IQR) are both measures of spread, also called measures of dispersion or scatter. They measure how much the data is spread out around the center point of the data set.

Hypothesis Testing for the Population Proportion

Hypothesis Testing

In this video we'll look at how to run a full hypothesis test, from beginning to end, or a proportion, instead of a mean. We'll also consider what it looks like to run this as a one-tail test and as a two-tail test.

Horizontal Line Test

Manipulating Functions

Learn to use the horizontal line test to determine whether or not a function is 1-to-1.

Dividing Rational Functions

Rational Expressions

In this video we learn how to divide rational expressions, which are fractional expressions in which both the numerator and denominator are polynomials. We'll turn the division problem into a multiplication problem by taking the reciprocal of the...Show More

Converting to Polar Coordinates

Polar & Parametric: Introduction to Polar Curves

In this video we'll learn to convert back and forth between rectangular (Cartesian) coordinates and polar coordinates. Rectangular coordinates are given as (x,y), where x is the horizontal distance from the origin and y is the vertical distance...Show More

Centroids of Plane Regions

Applications of Integrals: Geometry

In this video we'll look at how to find the centroid of a region. Think of the centroid as the center point of the region; it's the point at which you could perfectly balance the region on the tip of a pencil. Even when a region is irregularly...Show More