STAT 400 Lecture AL1 Examples for 8.1 (Part 2) Spring 2015 Dalpiaz Null Alternative H 0 : 0 vs. H 1 : < 0 H 0 : 2 02 vs. H 1 : 2 < 02 Left – tailed. H 0 : 0 vs. H 1 : > 0 H 0 : 2 02 vs. H 1 : 2 > 02 Right – tailed. H 0 : 0 vs. H 1 : 0 H 0 : 2 02 vs. H 1 : 2 02 Two – tailed. Test Statistic: 20221 sn n – 1 degrees of freedom Rejection Region: H 0 : 0 vs. H 1 : < 0 H 0 : 2 02 vs. H 1 : 2 < 02 Left – tailed. H 0 : 0 vs. H 1 : > 0 H 0 : 2 02 vs. H 1 : 2 > 02 Right – tailed.H 0 : 0 vs. H 1 : 0 H 0 : 2 02 vs. H 1 : 2 02 Two – tailed. 1. A machine at the Romano Drill Bit Company makes ½-inch ball bearings. When the machine is operating properly, the variance of the diameters of the bearings is at most 0.0003 inch 2. In a random sample of 41 bearings, the sample standard deviation of the diameters of the bearings was 0.02 inch. (Assume that the diameters of the bearings are approximately normally distributed.) a) Perform the appropriate test at a 5% level of significance. b) Perform the appropriate test at a 10% level of significance.2. Container-filling machines are used to package a variety of liquids, including milk, soft drinks, and paint. Ideally, the amount of liquid should vary only slightly, since large variations will cause some containers to be underfilled (cheating the customer) and some to be overfilled (resulting in loss for the manufacturer).The president of a company that developed a new type of machine boasts that this machine can fill 1-litter (1,000-cm 3) containers so consistently that the standard deviation of the fills will be less than 0.5 cm 3. To examine the validity of the claim, a random sample of 25 1-litter fills was taken, and the sample standard deviation was 0.4 cm 3. Test the president’s claim at the 5% significance level? 3. Metaltech Industries manufactures carbide drill tips used in drilling oil wells. The life of a carbide drill tip is measured by how many feet can be drilled before the tip wears out. Metaltech claims that under typical drilling conditions, the life of a carbide tip follows a normal distribution. Suppose that certain regulations require the variance of the lifetimes to be no more than 12 feet 2. Metaltech examines a random sample of 25 carbide tips to test whether these regulations are met. Suppose Metaltech decided to use a 5% level of significance and the observed sample mean is 30.5 feet with the sample variance 16 feet 2. Perform the appropriate
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