Answered: Michelle, a primary school teacher,…

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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Question

Michelle, a primary school teacher, administered an age-appropriate IQ test to all of her students in her class. The true population mean for the IQ test Michelle administered is 100, with a standard deviation of 15. Michelle discovered that the 25 students in her class scored 128 on average.

In order to examine whether Michelle's students scored differently compared to the general population, Michelle should use a Q1. ABCD. This test revealed that the mean IQ of Michelle's students was Q2. ABCD than that expected from children their age, Q3. ABCD = Q4. ABCD, Q5. ABCD. On the basis of this result, Michelle should decide to Q6. ABCD.

Possible answers for Q1:
A) a single sample t-test
B) a single sample z-test
C) a repeated measures t-test
D) an independent groups t-test

Possible answers for Q2:
A) significantly higher
B) no different
C) slightly higher
D) significantly lower

Possible answers for Q3:
A) t(25)
B) t(23)
C) t(24)
D) z

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

Given information:

The true population mean for the IQ test Michelle administered is 100, with a standard deviation of 15. Michelle discovered that the 25 students in her class scored 128 on average.

$\begin{array}{rcl} μ & = & 100, σ = 15 \\ \bar{x} & = & 128, n = 25 \end{array}$