5. A survey conducted at a Midwestern university and involving 1,500 students found that 68% had
taken out a student loan to help pay for the cost of their college education. A similar study at a
southeastern university in which 2,000 students were surveyed found that 47% had taken out a student
a.Develop and interpret a 95% confidence interval estimate for the difference in the proportions of
students who have loans at these two universities.
b.Using an alpha level of 0.05, test the hypothesis that there is no difference in the proportions of
students at these two universities who have loans. How does this test compare with the result you found
in part a?
c.The consistency of the diameters of wheel bearings is vital to the operation of the wheel. The
specifications require that the variance of these diameters be no more than 0.0015 centimeter squared.
The diameter is continually monitored by the quality-control team. Twenty subsamples of size 10 are
obtained every day. One of these subsamples produced bearings that had a variance of 0.00317
centimeter squared.Conduct a hypothesis test to determine if the quality control team should advise management to stop
production and search for causes of the inconsistency of the bearing diameters. Use a significance level
of 0.05. (Use p-value approach!)
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