Assume that two samples are independent simple random samples selected from norm

Question

Assume that two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Sample random samples high-interest (8 9%) mortgages and low-interest (6.3%) mortgages were obtained. For the 40 high-interest mortgages the borrowers had a mean credit score of 587.2 and a standard deviation of 12 For the 40 low-interest mortgages, the borrowers had a mean credit score of 794.3 and a standard deviation of 16.9. Use a 0.01 significance level to best the claim that the mean credit score of borrowers with high-interest mortgages is lower than the mean credit score of borrowers with low-interest mortgages. Does the credit rating score appear to affect mortgage payments? If so, how? Let mu_1 be the population mean credit score of borrowers with high-interest mortgages and let mu_2 be the population mean credit score of borrowers with low-interest mortgages. What are the null and alternative hypotheses? A. H_0: mu_1 > mu_2 H_1: mu_1 = mu_2 B. H_0: mu_1 mu_2 D. H_0: mu_1 mu _2 H_1: mu_1

Explanation / Answer

(a) Here hypothesises are

H0 : 1 = 2

Ha : 1 < 2

Option D is correct.

(b) Here mean credit score of borrowers with high interest mortagages x1 = 597.2

sample standard deviation s1 = 12.8

sample size n1 = 40

mean credit score of borrowers with high interest mortagages x2 = 794.3

sample standard deviation s2 = 16.9

sample size n2 = 40

pooles standard deviation sp = sqrt [s12 (n1 -1) + s22 (n2 -1)]/ (n1 +n2 -2) = sqrt [(12.82 *39 + 16.92 * 39)/78)]

sp = 14.99

so standard error of difference in means se0= sp * sqrt [1/n1 + 1/n2 ] = 14.99 * sqrt [ 1/40 + 1/40] = 3.352

so test statisitc

t = (x2 -x1 )/ se0 = (794.3 - 597.2)/ 3.352 = 58.80

P - value = 0.0000

Reject H0 . There is sufficent evidence to ssupport the claim the mean credit score of borrowers with high interest mortgages is lower than the mean credit score of borrowers with low- interest mortgages. The creidt rating score appear to affect mortgage payments. Mortgage payments for borrowers with low credit scores are significantly higher than the mortage payments for borrowers with high credit scores.

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