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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

credit score is used by credit agencies to assess the creditworthiness of individuals. Values range from 300 to 850, with a credit score over 700 considered to be a quality credit risk. According to a survey, the mean credit score is 712.8. A credit analyst wondered whether high income individuals (incomes in excess of $100,000 per year) had higher credit scores. He obtained a random sample of 24 high-income individuals and found the sample mean credit score to be 735.6 with a standard deviation of 74.5. Conduct the appropriate test to determine if high income individuals have higher credit

9. A credit score is used by credit agencies to assess the creditworthiness of individuals. Values
range from 300 to 850, with a credit score over 700 considered to be a quality credit risk.
According to a survey, the mean credit score is 712.8. A credit analyst wondered whether high
income individuals (incomes in excess of $100,000 per year) had higher credit scores. He
obtained a random sample of 24 high-income individuals and found the sample mean credit
score to be 735.6 with a standard deviation of 74.5. Conduct the appropriate test to determine
if high income individuals have higher credit scores at the a = 0.05 level of significance.
(a) State the null and alternative hypotheses:
Ho:
H₁:
(b) Identify the t-statistic:
to:
(2 decimals)
(c) Identify the P-value:
P-value:
(3 decimals)
(d) The results of the hypothesis test:
(A) Reject the null hypothesis
(B) Fail to reject the null hypothesis
(e) Interpret the results:
(A) There is sufficient evidence to support the claim that the mean credit score of high
income individuals is greater than 712.8.
(B) There is insufficient evidence to support the claim that the mean credit score of high
income individuals is greater than 712.8.
(C) There is sufficient evidence to support the claim that the mean credit score of high
income individuals is equal to 712.8.
(D) There is insufficient evidence to support the claim that the mean credit score of high
income individuals is equal to 712.8.

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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