A professor at a community college claims that a college algebra student can increase his or her score on an exam if the person is provided with a pre-test the week before the exam. To test her theory, she selected 16 college algebra students at random and gave these students a pre-test the week before an exam. She also selected a random sample of 12 students who were given the same exam but did not have access to a pre-test. The first group had a mean score of 79.4 with standard deviation 8.8. The second group had a mean score of 71.2 with standard deviation 7.9. Test to see if the population mean score of students who get a pre-test is different from the population mean score of those who do not. Use a 5% significance level.

Answered: A professor at a community college…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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A professor at a community college claims that a college algebra student can increase his or her score on an exam if the person is provided with a pre-test the week before the exam. To test her theory, she selected 16 college algebra students at random and gave these students a pre-test the week before an exam. She also selected a random sample of 12 students who were given the same exam but did not have access to a pre-test. The first group had a mean score of 79.4 with standard deviation 8.8. The second group had a mean score of 71.2 with standard deviation 7.9. Test to see if the population mean score of students who get a pre-test is different from the population mean score of those who do not. Use a 5% significance level.

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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