The recent default rate on all student loans is 5.6 percent. In a recent random sample of 300 loans at private universities, there were 10 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 α = .010?
The recent default rate on all student loans is 5.6 percent. In a recent random sample of 300 loans at private universities, there were 10 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 α = .010?
(a-1) Choose the appropriate hypothesis.
- H0: ππ ≥ .056; H1: ππ < .056. Accept H0 if z < –2.326
- H0: ππ ≥ .056; H1: ππ < .056. Reject H0 if z < –2.326
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a
-
b
(a-2) Calculate the z-score for the sample data using a left-tailed test at α = .01. (A negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
zcalc
(a-3) Should the null hypothesis be rejected?
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Yes
-
No
(b) Calculate the p-value. (Round your answer to 4 decimal places.)
p-value
(c) The assumption of normality is justified.
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Yes
-
No
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