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Hypothesis Testing 1. A manuiacturer has developed a new fishing line, which he claims has a mean breaking strength of at least 15 kilograms with a standard deviation of 0.5 kitograms. Test the hypothesis that ,u a 15 kilograms against the alternative that p c: 15 kilograms, a random sample of 50 lines will be tested. Use a: = {1.05. . Consider the null and alternative hypotheses H\" 5 12d and HH \":2 120. A random sample of 31 observations taken from this population produced a sample mean of 123.5 and a sample standard deviation of 15. If this test is made at 2.5% significance level, would you reject the null hypothesis? . In a certain city, a random sample of 55 eight-grade students has a mean score of 265 with a standard deviation of 55 on a national mathematical assessment test. This prompt a state school administrator to declare that the mean score of the state's eight-grade examination is more than 260. At a = {1.04, is there enough evidence to support the administrator's claim? . An environmentalist claim that the mean waste recycled by American adults is more than 1 pound per person per day. You want to test this claim. You find that the mean waste recycled per person per day tor a random sample of 12 American adults is 1.2 pounds. And the standard deviation is 0.3 pound. At a: = 0.05. can you support the claim? Assume that the population is normal. . The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council. you want to test this claim. A random sample of the number of classroom hours tor full time faculty tor one week is listed below. At a = 0.01. can you reject the dean's claim? Assume that the population is normal. 11.3 3.6 12.6 7.9 6.4 10.4 13.6 9.1