A credit score is used by credit agencies (such as mortgage companies and banks) 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 703.8 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 32 high-income individuals and found the sample mean credit score to be 718.9 with a standard deviation of 80.3 Conduct the appropriate test to determine if high-income individuals have higher credit scores at the a=0.05 level of significance. State the null and alternative hypotheses. Upper H0: muμ ▼ greater than> equals= less than< not equals≠ nothing Upper H1: muμ ▼ not equals≠ equals= greater than> less than< nothing (Type integers or decimals. Do not round.) Identify the t-statistic. t0=nothing (Round to two decimal places as needed.) Identify the P-value. P-valueequals=nothing (Round to three decimal places as needed.) Make a conclusion regarding the hypothesis. ▼ Fail to reject Reject the null hypothesis. There ▼ is is not sufficient evidence to claim that the mean credit score of high-income individuals is ▼ greater than equal to less than nothing.

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Description: A credit score is used by credit agencies (such as mortgage companies and banks) 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 surv

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A credit score is used by credit agencies (such as mortgage companies and banks) 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

703.8

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

high-income individuals and found the sample mean credit score to be

718.9

with a standard deviation of

80.3

Conduct the appropriate test to determine if high-income individuals have higher credit scores at the

a=0.05

level of significance.

State the null and alternative hypotheses.

Upper H0:

muμ

▼

greater than>

equals=

less than<

not equals≠

nothing

Upper H1:

muμ

▼

not equals≠

equals=

greater than>

less than<

nothing

(Type integers or decimals. Do not round.)

Identify the t-statistic.

t0=nothing

(Round to two decimal places as needed.)

Identify the P-value.

P-valueequals=nothing

(Round to three decimal places as needed.)

Make a conclusion regarding the hypothesis.

▼

Fail to reject

Reject

the null hypothesis. There

▼

is not

sufficient evidence to claim that the mean credit score of high-income individuals is

▼

greater than

equal to

less than

nothing.

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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