The mean breaking strength of a certain type of fiber is required to be at least 200 psi. Past experience indicates that the standard deviation of breaking strength is 5 psi. If a sample of 8 pieces of fiber yielded breakage at the following pressures, 210 198 195 202 197.4 196 199 195.5 would you conclude, at the 5 percent level of significance, that the fiber is unacceptable? What about at the 10 percent level of significance?

ST 701 Week Four Notes MaLyn Lawhorn September 5, 2017 and September 7, 2017 Independence In words, events A and B are said to be independent if knowledge that B occurred doesn’t change our uncertainty about A. Mathematically, this can be written as if P(B) > 0, then A and B are independent events if P(AjB) = P(A). However, this deﬁnition makes it appear as if direction matters. It sounds as if A being independent from B is not the same as B being independent from A, but this is not the case. A more formal, but less intuitive, mathematical deﬁnition of independence is if A and B are in- dependent events, P(A [ B) = P(A)P(B). In many problems, we can associate the word inde- pendence with the action of multiplying probabilitie