Question

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.

Answer 1

Given :

Sample mean,
`$\overline x = 714.2$`

Sample size, n = 40

Standard deviation, s = 83.2

∴ The null hypothesis is
`$H_0 : \mu = 703.5$`

Alternate hypothesis is
`$H_a : \mu > 703.5$`

Test statistic :

`$z = (\overline x - \mu)/(s / \sqrt n)$`

`$z = \frac{714.2-703.5}{83.2 / \sqrt {40}}$`

z = 0.813

Now at α = 0.05, for a right tailed,

`$z_(critical) = 1.645$`

Since,
`$z < z_(critical)$` , we fail to reject the null hypothesis.