2- A drink vending machine is adjusted so that, on average, it dispenses 220 mls of fruit juice (with a standard deviation of 10mls) into a plastic cup. However, the machine has a tendency to go out of adjustment and periodic checks are made to determine the average amount of fruit juice actually being dispensed. A sample of 45 drinks is taken to test the adjustment of the machine. For a-5%, an appropriate decision rule would be (a) -3.75 (c) -2.50 (b) -0.83 2.50 (d) 3 3- A tyre manufacturer claims that its tyres have a mean life of at least 50 000 kms. A random sample of 16 of these tyres is tested and the sample mean is 33 000 kms. Assume the populations standard deviation is 3000 kms and the lives of tyres are approximately normally distributed. To test the manufacturer's claim using the 5% level of significance the analyst should use a one tail test in the right tail and the test (b) statistic Z use a one tail test in the left tail and the statistic t (a) (c) use a one tail test in the left tail and the test statistic Z (d) use a two tail test and the test statistic t 4 Joan's Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost- estimating purposes, managers use two hours of labor time for planting of a medium- sized tree. Actual times from a random sample of 10 plantings during the past month follow (times in hours). 1.7 1.5 2.6 2.2 2.4 2.3 2.6 3.0 1.4 2.3 With a 0.05 level of significance, Use the following steps to test to see whether the population mean tree planting time differs from two hours. Answer the following questions: a- What type of test are you performing? (a) Hypothesis Test for One Sample Mean (b) Hypothesis Test for One Sample Proportion (c) Hypothesis Test for One Sample Variance/Standard Deviation (d) None of the above b- What are the null and alternative hypothesis for this test (a) Hou=2, H:μ #2 (b) Hou=2, H₁: <2 (c) Hou=2, Hi: <2 (d) Hop <2, Hip # 2 c- The test statistic value is (a) t=1.23 (b) t= 2.262 © z=1.96 (d) None of the above d- the tabulated value is (b) t=1.23 z=1.96 e- P_value is (c) 0.125 ©0.250 (b) t=2.262 (d) Z=1.96 (b) 0.025 (d) 0.05 f- Using 0.05 as a level of significant, the decision is (d) Reject H0 (a) Reject H1 (b) Cannot reject HO (d) Information is not enough