Quiz: QuizCh9.2-Ch9.4 Sp17 This Question Assume that the two samples are indepen
ID: 3251948 • Letter: Q
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Quiz: QuizCh9.2-Ch9.4 Sp17 This Question Assume that the two samples are independent andam samples selected em smple random samples interest 7 and m Does the and a standard de 163 Use a001 For the 40 sigMcance level to test the clam there the motgage payments Let w, be the population mean cseda score of bomowers with high interest mengages and let be the population mean crede score of borrowers ir lo enrrest mortgages What Mrpothese alculate the test Make conclu on about hypothesis and snal conclusion that ada sees the clum the mengage payments borowers high een This Quiz: 23 pts potExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: High interest = Low interest
Alternative hypothesis: High interest < Low interest
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 3.22
DF = 78
t = [ (x1 - x2) - d ] / SE
t = - 63.57
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 0.67. We use the t Distribution Calculator to find P(t < 0.67) = less than 0.00001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
Reject H0, From the above test we have sufficient evidence in the favor of the claim that mean credit score of borrower with high interest mortgages is lower than the mean credit score of borrowers with low interest mortgages.
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