The recent default rate on all student loans is 6.8 percent. In a recent random

Question

The recent default rate on all student loans is 6.8 percent. In a recent random sample of 293 loans at private universities, there were 11 defaults.

Does this sample show sufficient evidence that the private university loan default rate is below the rate for all universities, using a left-tailed test at ? = .010?

Calculate the z-score for the sample data using a left-tailed test at ? = .01. (A negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

The recent default rate on all student loans is 6.8 percent. In a recent random sample of 293 loans at private universities, there were 11 defaults.

Does this sample show sufficient evidence that the private university loan default rate is below the rate for all universities, using a left-tailed test at ? = .010?

Explanation / Answer

Answer to the question is as follows:

a-1)

p = .068
n = 293
x = 11
p^ = x/n = 11/293 = 0.0375

Ho: p>=.068
Ha: p<.068

.010 refers to a Z of -2.326

So, Reject Ho if Z<-2.326, Hence, option b. is Correct

a2) Z-calc = (p^-p)/sqrt(p*p'/n) = (.0375-.068)/sqrt(.068*.932/293) = -2.074

by the way, since Z-calc is not < than -2.326 we fail to reject Ho

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