Answered: Two statistics professors at two rival…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Two statistics professors at two rival schools decide to use IQ scores as a measure of how smart the students at their respective schools are. IQ scores are known to be Normally distributed. The two professors will use this knowledge to their advantage. They will randomly select 10 students from their respective schools and determine the students' IQ scores by means of the standard IQ test. The two professors will use the pooled version of the two-sample t test to determine whether the students at the two universities are equally smart. Let μ₁ and μ₂ represent the mean IQ scores of the students at the two universities.Let σ₁ and σ₂ be the corresponding population standard deviations. The hypotheses they will test are H₀: μ₁ – μ₂ = 0 versus H_a: μ₁ – μ₂ ≠ 0. Based on the two samples of 10 students, the two professors find the following information: = 111, = 120, s₁ = 7, and s₂ = 11.

Reference: Ref 7-20

What is the value of the test statistic?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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