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A product developer is investigating the tensile strength of a new synthetic fiber that will be used to make a cloth. Strength is usually affected by the percentage of cotton used in the blend of materials for the fiber. The engineer conducted a completely randomized experiment with five levels of cotton content and replicates the experiment five times. The data are shown in the following table. Cotton weight Sum percent Observation Vi. 15 7 7 15 11 9 49 20 12 17 12 18 18 77 25 14 19 19 18 18 88 30 19 25 22 19 23 108 35 7 10 11 15 11 54 Yj = V. = 376.00 yi = 6292 (a) Is there evidence to support the claim that cotton content affects the mean tensile strength? Use a = 0.05. (b) Suppose that the experimenter feels that the standard deviation of each treatment is the one that can be estimated by error (use the result from the above ANOVA to get an estimate of the standard deviation). The experimenter wishes to reject the null hypothesis with a probability at least 0.9 if the two treatments mean differed by as much as 10 units. Is the sample size n = 5 used in the experiment enough to meet the wishes of the experimenter? (Show your detail calculation and procedure you applied.)