Answered: Can the economist conclude that the…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 4SE: What is the difference between events and outcomes? Give an example of both using the sample space...

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Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from

300

850

, with a score of

720

or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO score is more than the cutoff of

720

. She finds that a random sample of

120

people had a mean FICO score of

740

with a standard deviation of

. Can the economist conclude that the mean FICO score is greater than

720

? Use the

=α0.01

level of significance and the

-value method with the

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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good credit: the fair isaac corporation (fico) credit score is used by banks and other lenders to determine whether someone is a good credit risk. scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. an economist wants to determine whether the mean fico score is more than the cutoff of 720. she finds that a random sample of 90 people had a mean fico score of 730 with a standard deviation of 91. can the economist conclude that the mean fico score is greater than 720? use the a=0.05 level of significance and the critical value method.

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