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A Fair Isaac Corporation (FICO) 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 FICO score over 700 considered to be a quality credit risk. According to Fair Isaac Corporation, the mean FICO score is 703.5. 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 40 high-income individuals and found the sample mean credit score to be 714.2 with a standard deviation of 83.2. Conduct the appropriate test to determine if high-income individuals have higher FICO scores at the \alpha=0.05α=0.05 level of significance.

Sagot :

Solution :

Given :

Sample mean, [tex]$\overline x = 714.2$[/tex]

Sample size, n = 40

Standard deviation, s = 83.2

∴ The null hypothesis is [tex]$H_0 : \mu = 703.5$[/tex]

   Alternate hypothesis is [tex]$H_a : \mu > 703.5$[/tex]

Test statistic :

[tex]$z = \frac{\overline x - \mu}{s / \sqrt n}$[/tex]

[tex]$z = \frac{714.2-703.5}{83.2 / \sqrt {40}}$[/tex]

z = 0.813

Now at α = 0.05, for a right tailed,

[tex]$z_{critical} = 1.645$[/tex]

Since, [tex]$z < z_{critical}$[/tex] , we fail to reject the null hypothesis.

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