Answered: To estimate the benefits of an SAT prep…

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

To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected. For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their exit score on the exam they take at the end of the course is recorded as well. The table displays the scores.

The mean of the differences is 193 points, and the standard deviation of the differences is 62.73 points. The conditions for inference are met. A 98% confidence interval for the mean difference (after – before) in score is 137.04 points to 248.96 points. What is the correct interpretation of this interval?

98% of students in this sample increased their score, on average, by 137.04 to 248.96 points.

98% of students who take this course will increase their score, on average, by 137.04 to 248.96 points.

The school can be 98% confident that students who take this course increase their SAT score, on average, by 137.04 to 248.96 points.

The school can be 98% confident that the students in the sample increased their SAT score, on average, by 137.04 to 248.96 points.

Student
1
2
4
6
7
8
10
Before
800
870
860
820
1140
1050
850
910
830
1140
After
1100
1010
1000
980
1410
1270
1020
1010
1060
1340

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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