Question 461981: The recent default rate on all student loans is 5.2 percent. In a recent random sample of 300 loans at private universities there were 9 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 = .01?
(a-1) Choose the appropriate hypothesis.
(a-2)
What is the z score for the sample data? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
z value
(a-3) Should the null hypothesis be rejected?
(b) Calculate the p-value. (Round your answer to 4 decimal places.)
p-value
(c) The assumption of normality is justified.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The recent default rate on all student loans is 5.2 percent. In a recent random sample of 300 loans at private universities there were 9 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 = .01?
(a-1) Choose the appropriate hypothesis.
Ho: p >= 0.052
Ha: p < 0.052
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(a-2)
What is the z score for the sample data? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
test statistic::: z(9/300) = ( 0.03-0.052)/sqrt[0.052*0.948/300] -1.7162
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(a-3) Should the null hypothesis be rejected?
p-value = P(z < -1.7162) = 0.0431
Since the p-value is greater than 1%,
fail to reject Ho at the 1% level.
(b) Calculate the p-value. (Round your answer to 4 decimal places.)
p-value
Done
(c) The assumption of normality is justified.
I'll leave that to you. Check your textbook.
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Cheers,
Stan H.
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