When consumers apply for credit, their credit is rated using FICO scores. You ar

Question

When consumers apply for credit, their credit is rated using FICO scores. You are thinking of opening a cell phone store and hire a consultant to find an area with a demographic of people who can afford the high end phones you will sell. The consultant claims in the area he recommends that FICO scores exceed the 670 you require. You are skeptical and have a friend sample 25 people. She finds a mean FICO score of 678 with a standard deviation of 20. Test the consultants claim at the .05 significance level. Be sure to show the claim and the null and alternative hypothesis. What do you conclude about the null hypothesis? Do you believe the consultant?

Explanation / Answer

Laying out the whole problem from the start:

Ho: Mu <= 670

Ha: Mu > 670

Stdev =20

n = 25

t = (678-670)/(20/sqrt(25)) = 2

We have used t as n<25

So, df = n-1=24

So, the pvalue is .02847.

The result is significant at p < .05.

We reject null and support the claim of the consultant and conclude that:

" The consultant claim that the FICO scores exceed 670 is true"

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