o determine if his teaching method increases students’ learning, a professor administers a pretest to his class at the beginning of the semester and then a posttest at the end of the semester. The results from 10 randomly chosen students are given below. Let Population 1 be the Pretest scores and Population 2 be the Posttest scores. Test Scores Pretest Posttest 83 71 73 72 82 81 81 57 97 88 57 56 53 51 68 59 57 60 90 84 Step 2 of 2 : Interpret the confidence interval obtained in Step 1. 1. We are 90% confident that the mean increase in students scores from the pretest to the post test is between 1.7 and 10.7 points for the population of students in this professors class. 2. Since the confidence interval contains zero, the data do not provide evidence of a significant increase in students scores using the professors teaching method at a 90% confident level. 3. Since the confidence interval does not contain zero, the data provides evidence of a significant increase in students scores using the professors teaching method at a 90% confident level. 4. We are 90% confident that the mean decrease in students scores from the pretest to the post test is between 1.7 and 10.7 points for the population of students in this professors class.

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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To determine if his teaching method increases students’ learning, a professor administers a pretest to his class at the beginning of the semester and then a posttest at the end of the semester. The results from 10 randomly chosen students are given below. Let Population 1 be the Pretest scores and Population 2 be the Posttest scores.

Test Scores

Pretest	Posttest
83	71
73	72
82	81
81	57
97	88
57	56
53	51
68	59
57	60
90	84

Step 2 of 2 : Interpret the confidence interval obtained in Step 1.

1. We are 90% confident that the mean increase in students scores from the pretest to the post test is between 1.7 and 10.7 points for the population of students in this professors class.

2. Since the confidence interval contains zero, the data do not provide evidence of a significant increase in students scores using the professors teaching method at a 90% confident level.

3. Since the confidence interval does not contain zero, the data provides evidence of a significant increase in students scores using the professors teaching method at a 90% confident level.

4. We are 90% confident that the mean decrease in students scores from the pretest to the post test is between 1.7 and 10.7 points for the population of students in this professors class.

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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