Answered: A new approach for teaching mathematics…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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A new approach for teaching mathematics was introduced that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the performances the new approach students with those taught using a traditional curriculum. During the study, students in both classes that used the new approach and traditional classes took a Algebra test that did not allow them to use calculators. The accompanying table shows the results. Are the mean scores of the two groups significantly different?

Write appropriate hypotheses. Let μN be the mean Algebra test score for students in classes that use the new approach. Let μT be the mean Algebra test score for students in traditional classes.

b) Do you think the assumptions for inferences are satisfied? Explain.

No. The students within each class are not independent individuals as their score on the Algebra test is dependent upon other students in the class.

No. The groups are not large enough and thus cannot be used to make inferences upon the population.

Yes. The groups are independent, though it is not certain if students were randomly assigned to each class. However, the sample sizes are large enough that the Central Limit Theorem applies.

Yes. The groups are small enough that the results can be inferred upon the population without risk of incorrect conclusions being made.

Part 3

c) Refer to the computer output for the hypothesis test. Explain what the P-value means in this context. Choose the correct answer below.

If the means for the two classes are actually equal, there is less than a 1 in 10,000 chance of seeing a difference as large as or larger than the observed difference just from natural sampling variation.

There is less than a 1 in 10,000 chance that these results are incorrect and they should be accepted as true.

If the means for the two classes are actually unequal, there is more than a 1 in 10,000 chance of seeing a difference as large as or larger than the observed difference just from natural sampling variation.

Part 4

d) State the conclusion of this test.

On average, students who learn in the new class method do significantly better on Algebra tests that do not allow them to use calculators than students who learn by traditional methods.

Students who learn in the tradition method will always perform better on Algebra tests that do not allow the use calculators than students who are in the new class.

On average, students who learn in the new class method do significantly worse on Algebra tests that do not allow them to use calculators than students who learn by traditional methods.

On average, students who learn in the new class method will receive a 29.0 average on Algebra tests that do not allow them to use calculators than students who learn by traditional methods.