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- A prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of active ingredient. The manufacturer periodically collects data to determine if the production process is working properly. A random sample of 64 pills has a mean of 250 ppm with a standard deviation of 12 ppm. Let u denotes the average amount of the active ingredient in pills of this allergy medicine. The null and alternative hypotheses are as Ho: μ = 245, Hau #245. The level of significance is 1%. The t-test statistic is 3.33 with a P-value of 0.0014. What is the correct conclusion? The mean amount of active ingredient in pills of this allergy medicine is greater than 245 ppm. The mean amount of active ingredient in pills of this allergy medicine is equal to 250 ppm. The mean amount of active ingredient in pills of this allergy medicine is equal to 245 ppm. moon amount of active ingredient in pills of this allergy medicine is not equal to 245 ppm.The quality characteristic of a product Y consists of three components X1, X2, and X3. The distributions of these components are normal with means 100, 2, 1 and variances 1, 1, 1 respectively. The specifications of the product are 90 ± 8. If Y= X1 + -7X2 + -9X3. Products that are below the lower specification limit are scrapped. Find the proportion of scrapped products = Ф(z).X is a normally normally distributed variable with mean u =10 and standard deviation a =4. Find A) P(x 1) C) P(103) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentileThe average wait time to get seated at a popular restaurant in the city on a Friday night is 12 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 13 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 13, 13, 11, 13, 13, 13, 13, 10, 12, 13, 13, 10, 13 What can be concluded at the the αα = 0.05 level of significance level of significance? The null and alternative hypotheses would be: H0 = (p,u) (<,>,=,not equal) to _____ H1 = (p,u) (<,>,=,not equal) to _____ The test statistic (t,z) = ___ The p-value = _____ Thus, the final conclusion is that ... The data suggest that the population mean wait time for men who wear a tie is not significantly more than 12 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 12. The data suggest the population mean is not significantly more than 12…الموافق foo an exponentiaL distribution fx Cx jt) e.w. where u>o Write (Dankderive) meancespedoed V9lue) f.eECx)The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630Let the test statistic T have at distribution when H, is true. Give the P-value for each of the following situations. (Round your answers to three decimal places.) n USE SALT (a) H: u > Ho, df = 13, t = 2.663 P-value = (b) H3: µ < Ho, n = 27, t = 2.131 P-value = (c) H: u # Ho, n = 41, t = -1.581 or t = 1.581 P-value =3.4 Solve the below problem: Let Y, and Y, have a bivariate normal distribution: 2. 1. 2. Y2-H2 exp 2no,02y1-p2 2(1-p2) {. (ज-र.) + ( ज-र) (ज-पदर) 07 (जब)} Dr= –00 < y, < ∞, -00 < y2 < ∞, Show that the marginal distribution of Y, is normal with mean µz and variance o is given by: 2, 1 f(y2) = 203 ,-00 < Y2 < ∞ 2.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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