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Refer to Exercise 46. Suppose the distribution of diameter is normal. a. Calculate P(11.99 ju}. But max (X,) = p iff X; Su for all i.] Compute a 97% CI for the true median amount of alanine for infants on such a diet ("The Essential Amino Acid Requirements of Infants," Amer. J. of Nutrition, 1964: 322-330). c. Let x 2) denote the second smallest of the x.s and 2.84 3.54 2.80 1.44 2.94 2.70 denote the second largest of the X.S. What is the confidence level of the interval c. Let x2) denote the second smallest of the x,'s and X(-1) denote the second largest of the x;'s. What is the confi- dence level of the interval (X(2) *(m-1)) for u?Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing H.: p = .5 versus H,: p # .5 based on a random sample of 25 individuals. Let the test statistic X be the number in the sample who favor the first company and x represent the observed value of X. a. Describe type I and II errors in the context of this problem situation. b. Suppose that x = 6. Which values of X are at least as contradictory to H. as this one? c. What is the probability distribution of the test statistic X when H, is true? Use it to compute the P-value when x = 6. d. If Ho is to be rejected when P-values .044, compute the probability of a type II error when p = 4, again when p = .3, and also when p = .6 and p = .7. [Hint: P-value > .044 is equivalent to what inequalities involving x (see Example 8.4)?] e. Using the test procedure of (d), what would you conclude if 6 of the 25 queried favored company 1?A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design. a. Define the parameter of interest and state the relevant hypotheses. b. Suppose braking distance for the new system is normally distributed with a = 10. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to Ho than 117.2, what is the P-value in this case, and what conclusion is appropriate if a = .10? c. What is the probability that the new design is not implemented when its true average braking distance is actually 1 1 5 ft and the test from part (b) is used