Discuss the below:
Q1 Calculate the test statistic and p-value for each sample.
a. H0: π ≥ .50 versus H1: π < .50, α = .025, p = .60, n = 90
Q2 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. (a) 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? (b) Calculate the p-value. (c) Verify that the assumption of normality is justified.
Q3 Find the p-value for each test statistic.
Two-tailed test, z=−1.69
Q4 Calculate the test statistic and p-value for each sample. State the conclusion for the specified α.
b. H0: μ ≥ 200 versus H1: μ < 200, α = .05, ¯x = 198, s = 5, n = 25
Q5 In 2004, a small dealership leased 21 Chevrolet Impalas on 2-year leases. When the cars were returned in 2006, the mileage was recorded (see below). Is the dealer's mean significantly greater than the national average of 30,000 miles for 2-year leased vehicles, using the 10 percent level of significance? Mileage
40,060 24,960 14,310 17,370 44,740 44,550 20,250
33,380 24,270 41,740 58,630 35,830 25,750 28,910
25,090 43,380 23,940 43,510 53,680 31,810 36,780