Question

A FICO score is used by credit agencies such as banks to determine whether to lend money and the interest rate to charge. Its value ranges from 300 to 850 and if you have a score over 700, you are considered to be a "quality" credit risk. The mean credit score of average income earners in Nevada is estimated by Fair Isaac to be 630. A recent survey of 21 high income earners in Nevada had a mean FICO score of ¯x=619 and a standard deviation of s=58. Use a 0.01 significance level to test the claim that the mean FICO score of high income earners in Nevada is equal to 630, the mean score of average income earners in Nevada.

Claim:

Opposite:

The test is:

The test statistic is:

What is the range of the P-value:

Based on this we?

Conclusion?

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

Claim: The mean FICO score of high income earners in Nevada is equal to 630.

Opposite: The mean FICO score of high income earners in Nevada is not equal to 630.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The mean FICO score of high income earners in Nevada is equal to 630.

Alternative hypothesis: H_a: The mean FICO score of high income earners in Nevada is not equal to 630.

H₀: µ = 630 versus H_a: µ ≠ 630

This is a two tailed test.

The test is: one sample t test

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 630

Xbar = 619

S = 58

n = 21

t = (Xbar - µ)/[S/sqrt(n)]

t = (619 - 630)/[58/sqrt(21)]

t = -11/ 12.6566

t = -0.8691

Test statistic = -0.8691

The test statistic is -0.8691.

df = n – 1 = 21 - 1 = 20

α = 0.01

Critical value = -2.8453 and 2.8453

(by using t-table or excel)

P-value = 0.3951

(by using t-table)

Range of P-value would be given as below:

0.10 < P-value < 0.50

P-value > α = 0.01

So, we do not reject the null hypothesis

Based on this we fail to reject the null hypothesis.

Conclusion:

There is sufficient evidence to conclude that the mean FICO score of high income earners in Nevada is equal to 630.