Demonstrates the basics of hypothesis testing using the P-value method: find the test statistic which in turn gives us the P-value, then compare the P-value to the level of significance (alpha) to determine whether or not the Null Hypothesis is rejected or not. PLEASE READ!! I did not make a mistake by showing .0045 as the area (probability) for 2.61. Look carefully at my picture. I have shaded to the **RIGHT** of 2.61, not to the left. If you look up 2.61 on your table and see .9955 your table is assuming you want the area shaded to the LEFT of 2.61. Again, I shaded to the RIGHT of 2.61. I hope that makes sense!
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Demonstrates to approximate a binomial probability distribution with a normal distribution. "Continuity correction" is explained. (Part 1 of 2)
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Finding the z-score that corresponds to a given Percentile (area shaded to the left of the z-score).
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How to find the area under a normal curve, given a z-value, shaded to the left, shaded to the right, and shaded in between.
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Describes how to find the Limits @ Infinity for a rational function to find the horizontal and vertical asymptotes.
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Demonstrates a simple Integration by Substitution example.
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Rational Expressions are simply fractions.... Fractions with Variables in them. So, given a rational expression, how do you find the value(s) that would make the expression Undefined? This video shows you how. It also briefly explains what is meant by "undefined."
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Demonstrates how to find the mean and standard deviation of discrete (countable) random variables BY HAND. It's long and tedious, and involves lots of steps. But, with time, and attention to detail, it can be done!
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Demonstrates how to find the slope of a tangent line using the difference quotient's definition of a derivative. Then, it shows how to use the slope of the tangent line, along with a given point to find the equation of the tangent line at that given point.
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Demonstrates how to find cutoff scores (z-scores) that correspond to a given %, assuming a standard normal distribution.
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This video demonstrates hypothesis testing using the P-value method. This example assumes you know sigma (the population standard deviation), so it's a z-test, NOT a t-test.
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Given that we have 10 eggs in a basket, 3 of which are cracked eggs, we will randomly choose 4 of the 10 eggs. This video demonstrates how to find the probability that (a) all three of the cracked eggs are selected, (b) none of the cracked eggs are selected, and (c) two of the cracked eggs are selected.
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Given a linear equation as the integrand, I demonstrate how to find the area under the "curve" using the formula for a Trapezoid, as well as using the Fundamental Theorem of Calculus. Both methods yield the same result.
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Demonstrates how to find the derivative of a given equation, which contains a trig function in it, that involves the use of Implicit Differentiation. It also uses the Product Rule and the Chain Rule.
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Demonstrates a definite integration using substitution, where the integrand has a square root in it.
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Demonstrates two problems where you need to use the Quotient Rule for derivatives, where the numerators and denominators both have trigonometric functions in them.
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Demonstrates how to find the derivative of (9x / 4x + 1)^6. Both the Chain Rule and the Quotient Rule are used in this example, as well as a calculator to find a large coefficient.
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How to create a MS Excel spreadsheet to determine the area (probability) under the normal curve instead of a table. Given a z-score, this shows how to find the prob shaded to the left of the z-score, shaded to the right of the z-score, and shaded in between two z-scores. It uses the Excel formula called "Normsdist()".
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This video describes the Pairwise Comparison Method of Voting. Each pair of candidates gets compared. The winner of each comparison is awarded a point. And the candidate with the most "points" is the winner. If there is a tie in the comparison, then each candidate gets 1/2 a point.
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This video walks through a hypothesis testing example using the critical value method. In this example, sigma (the population standard deviation) is known. So, it's a z-test, NOT a t-test. This is important!
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Demonstrates how to find the Mean (Expected Value) and Standard Deviation of discrete random variables using MS Excel (version 2007).
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Demonstrates how to evaluate a definite integral using the 1st Fundamental Theorem of Calculus, where the integrand is a quadratic equation.
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Two examples are shown using a Normal Distribution to approximate a Binomial Probability Distribution. In the first example we cannot approximate the binom dist with the normal dist. But in the second example we can.
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Demonstrates "Integration by Substitution" with a trickier problem. I forgot to show the check, so take the derivative of the answer I came up with, using the chain rule, and verify that it takes you back to the original integrand.
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Plurality-with-elimination method of voting is "the MAJORITY of 1st place votes". This means the winner must have more than 1/2 of the 1st place votes. If a candidate does not have a majority of 1st place votes, then the candidate with the least number of 1st place votes gets eliminated, and the rest of the candidates "move up". Now recount the 1st place votes. Keep repeating this process until a candidate eventually has the majority of first place votes.
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Demonstrates how to find the derivative of (tan x)(sec x) using the Product Rule. The answer is given in two equivalent forms.
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Shows how to rewrite an equation with a radical so that it looks like exponential form, then converting the exponential form into Logarithmic form.
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This video shows how (& why) to simplify rational expressions with "opposite terms" such as (6 - p) / (p - 6).
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Demonstrates how to find the first derivative (slope of tangent line) at a given point. And shows how to find the equation of the tangent line after finding the slope, at some given point.
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Demonstrates how to integrate an integrand of (1/u) using natural logarithms. This is a simple introduction to the integration of a transcendental function.
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Demonstrates how to find the Total Area and Net Area between an absolute value function and the x-axis.
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Demonstrates how to add and subtract rational expressions by first finding the LCD, then changing each fraction to match its new denominator, then simplifying the result.
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