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Use the 5 steps to solve please outline and break problem to each step 2. Credit

ID: 3324270 • Letter: U

Question

Use the 5 steps to solve please outline and break problem to each step 2. Credit scorecards are used by financial institutions to help decide to whom loans should be granted. An analysis of the records of a random sample of loans at one bank produced the following results Score Under 600 Score 600 or More Sample size 804 562 Number defaulted Do these results allow us to conclude that those who score under 600 have higher default rate than those who score 600 or more? Use a 5% significance level, what is p-value?

Explanation / Answer

p1 = 11/562 = 0.02

P2 = 7/804 = 0.009

H0: p1 = p2

H1: p1 > p2

The Pooled sample proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2)

= (0.02 * 562 + 0.009 * 804)/(562 + 804)

= 0.0135

SE = sqrt (P * (1 - P) * (1/ n1 + 1/n2))

= sqrt (0.0135 * 0.9865 * (1/562 + 1/804))

= 0.0063

The test statistic Z = (p1 - p2)/SE

= (0.02 - 0.009)/0.0063 = 1.75

P-value = P(Z > 1.75)

= 1 - P(Z < 1.75)

= 1 - 0.9599 = 0.0401

As the p-value is less than the significance level (0.0401 < 0.05), so the null hypothesis is rejected.

So there is sufficient evidence to support the claim that those who score under 600 have higher default rate than those who score 600 or more.