Hypothesis Testing with Binomial Distribution by Neil

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2017-05-25 21:39

Probability & Statistics

This example demonstrates hypothesis testing using the binomial distribution. It involves key mathematical concepts such as the binomial distribution, hypothesis testing, and combinatorics. Using GeoGebra commands like Sequence and BarChart, it constructs a binomial distribution probability bar chart and simulates hypothesis testing. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

Sequence(((Binomial[n, r] * p^(r)) * (1 - p)^(n - r)), r, 0, n) → L
BarChart(-0.5, n + 0.5, L) → a
Sequence(Sum[L, i], i, 1, n + 1) → S
BarChart(-0.5, c_1 + 0.5, Take[L, 1, c_1 + 1]) → c
BarChart(c_2 - 0.5, n + 0.5, Take[L, c_2 + 1, n + 1]) → d
BarChart(-0.5, c_3 + 0.5, Take[L, 1, c_3 + 1]) → f
Element(S, c_3 + 1) → s_3
BarChart(c_4 - 0.5, n + 0.5, Take[L, c_4 + 1, n + 1]) → g
Segment(A, B) → i
Point(i) → X
Segment((x(X), 0.3), (x(X), -0.1)) → j
BarChart(-0.5, x(X) + 0.5, Take[L, 1, x(X) + 1]) → k
Element(S, x(X) + 1) → x_1
BarChart(x(X) - 0.5, n + 0.5, Take[L, x(X) + 1, n + 1]) → l
Element(S, c_1 + 1) → s_1

AI Drawing Prompt Reference

Draw a binomial distribution probability bar chart with the horizontal axis representing the number of successes. First, plot the full distribution bars. Then, using two critical values, highlight the left and right rejection regions in different colors, and display their cumulative probabilities. Add a horizontal segment above the chart with a movable point representing the test statistic; draw a vertical line from this point downward, shading the left and right areas separately, and show the cumulative probability for this point.

The prompt above was compiled from the original drawing commands and is for reference only.