Answered: SAT Scores. The College Board SAT…

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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SAT Scores. The College Board SAT college entrance exam consists of three parts:
math, writing, and critical reading. Sample data showing the math and writing scores
for a sample of 12 students who took the SAT follow.

Student Math Writing
1 540 474

2 432 380

3 528 463

4 574 612

5 448 420

6 502 526

7 480 430

8 499 459

9 610 615

10 572 541

11 390 335

12 593 613

Question :

a. Use a .05 level of significance and test for a difference between the population
mean for the math scores and the population mean for the writing scores. What is
the p-value and what is your conclusion?
b. What is the point estimate of the difference between the mean scores for the two
tests? What are the estimates of the population mean scores for the two tests?
Which test reports the higher mean score?

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 + ...

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