1. The mean breaking strength of a certain type of fiber is required to be larger than 200 psi. Past experience has shown that we can assume that the breaking strength is normally distributed with standard deviation σ = 4.5 psi. A sample of 8 fibers yielded breakage at the following pressures (in psi): 210, 206, 198, 202, 201, 198, 199, 205. (a) Formulate a null hypothesis versus an alternative hypothesis to verify that this type of fiber is acceptable. (b) Compute a test statistic to test the hypotheses from part (a). (c) Based on the value of the test statistic in part (a): (i) give the conclusion at α = 5%; (ii) give the conclusion at α = 10%. (d) Suppose that a sample of 30 fibers yielded a mean breakage of ¯x = 202.375 psi. For this new study, compute a test statistic to test the hypotheses from part (a) and give the conclusion at α = 5%.
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(a) Formulate a null hypothesis versus an alternative hypothesis to verify that this type of fiber is acceptable.
(b) Compute a test statistic to test the hypotheses from part (a).
(c) Based on the value of the test statistic in part (a): (i) give the conclusion at α = 5%; (ii) give the conclusion at α = 10%.
(d) Suppose that a sample of 30 fibers yielded a mean breakage of ¯x = 202.375 psi. For this new study, compute a test statistic to test the hypotheses from part (a) and give the conclusion at α = 5%.
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