Math Problem Statement

  1. A principal claims that 70% of Advanced students in mathematics are male. Teacher X would like to investigate if this is true. She randomly selected 22 students and found out that 12 of them are males. Run a binomial test to determine if there is enough evidence to suggest that the proportion of male Advanced students is not the same to what the principal claim. Use alpha = 0.05

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
Binomial Distribution
Proportion Testing

Formulas

Binomial test formula for proportion testing: P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Calculation of p-value in hypothesis testing

Theorems

Central Limit Theorem (for approximation)
Binomial Theorem (underlying distribution)

Suitable Grade Level

College Level