When working properly, a cereal packaging machine is supposed to place 16 ounces of cereal in each box. A random sample of 10 boxes gave the following weights: 15.3, 16.1, 16.3, 15.2, 15.6, 16.4, 15.9, 15.0, 14.8, 15.1. Assuming the data are from a normal distribution, state appropriate hypotheses and perform the appropriate test. What can we conclude?
Female killdeers usually lay four eggs each spring. It is suspected that the average weight of the first-hatched birds will exceed the average weight of the last-hatched birds. Suppose that in eight broods, the following differences (first-hatched minus last-hatched) in weights are observed: 0.02, -0.10, 0.06, 0.23, 0.14, 0.14, -0.04, 0.29. Assume the date are from a normal distribution. Does the data support the hypothesis that there is a difference between the average weights? State the hypotheses, perform the test, and state your conclusion.
R. A. Fisher investigated the results of testing two sleeping drugs on ten patients.The additional hours of sleep obtained from drug A instead of drug B were reported to be: 1.2, 2.4, 1.3, 1.3, 0.0, 1.0, 1.8, 0.8, 4.6, 1.3. Assume the data are from a normal distribution. Test the hypothesis that the mean number of additonal hours of sleep is 0. Again, clearly state your hypotheses, perform the test, and state you conclusion.