a 17) Find the critical value (t) for a sample with n = 10 and α = 0.05 if Ho: μ > 20. A) 1.833 B)-1.833 O C) 1.812 D) -1.812
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- EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.3.) A population has a mean of 300 and a variance of 80. If we get 160 samples from this population, what will be the mean and standard deviation of the sampling distribution of sample mean? A.) µx = 300 and ox =0.53 B.) µx = 300 and ox =0.71 C.) µx = 300 and ox =6.32 D.) µx = 300 and ox =80 %3D %3D %3D %3D 4.) The average price of fishes in the market is P142.23 with standard deviation of P46.24. If we take 49 samples from the market, what would be the mean and standard deviation of the sampling distribution of sample mean? A.) ux = 46.24 and ox = 49 B.) ux = 46.24 and ox = 6.61 C.) ux = 46.24 and ox = 20.32 D.) ux = 142.23 and ox =6.61 %3D %3DQn5. Using the Kruskal-Wallis test at a = 0.01, can we conclude that the three populations represented by the three samples differ with respect to propellant burning rates? A Summarized data is given as follows: For System I: , = 5, Sum of the ranks i.e., R = 47 For System II:2, = 6, Sum of the ranks i.e., R, = 16 For System III: n, = 8, Sum of the ranks i.e., R = 57. ( Given that Table value of Chi Square = 9.21)
- Qn5. Using the Kruskal-Wallis test at a= 0.01, can we conclude that the three populations represented by the three samples differ with respect to propellant burning rates? A Summarized data is given as follows: For System I m =5, Sum of the ranks i.e., R, = 58 For System II:n, = 6, Sum of the ranks i.e., R, 24 For System III: n, = 8, Sum of the ranks i.e., R 87. ( Given that Table value of Chi Square = 9.21) %3DQn5. Using the Kruskal-Wallis test at a = 0.01, can we conclude that the three populations represented by the three samples differ with respect to propellant burning rates? A Summarized data is given as follows: For System I: n = 5, Sum of the ranks i.e., R = 58 For System II:n, = 6, Sum of the ranks i.e., R, = 24 For System III: n, = 8, Sum of the ranks i.e., R, = 87. %3! ( Given that Table value of Chi Square = 9.21)(11.)Perform the test of hypotheses indicated, using the data from independent samples given. Use the p value approach. (The p-value can be only approximated.) a. Test Ho : H - Hz = 50 vs. Ha : µ, - u, > 50 @a = 0.01: = lu n1 = 30, x1 = 681 s1 = 8 n2 = 27, T2 = 625, 82 = 8 %3D b. Test Ho : 41 – Hz = 35 vs. Ha : Hi – Hy # 35@a = 0.10: n1 = 36, T1 = 325, 81 = 11 n2 = 29, T2 = 286. s2 = 7
- Determine the sample size needed to estimate μ for the given situation E = 4, σ = 35, (1 - α) = 0.90 4 295 207 208Determine U-x and population and sample A = 81 0=18 ox from the given parameters n = 36 size. of the1.7:19. For given set of numerical data, the following results are obtained P123=0:65 n = 15
- Determine lz and oz from the parameters of the population and the sample size a. μ- 80, σ-4, η- 49 b. μ= 52 σ= 10, η = 21 C. H 27, o = 6, n = 15 Answer part a. Hi = ;O = part b. Hz = (two decimal places) part c. lz = ; στ (two decimal places)EXER 6.3 Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 6 0 28 6 1 28 2 0 333333 28 28 28 2120 28 02. Suppose that a sample of size 10, (Xị, Yi), i = 1,2, .., 10 was collected to study the relationship between x and y. From the sample data, the following information was obtained. Xi 4 7 10 12 15 18 20 21 25 ei 3. 3 -2 -2 -7 -3 3 -2 7 Di = -3.18 + 2.49x a) Use a t-test approach to determine whether or not there is a significant relationship between x and y at 10% level. b) Construct and interpret a 90% interval estimate of E(y) at x. c) Find the standard error of the point estimator of the model intercept, S. d) Calculate and interpret the coefficient of determination. 20°C Mostly s...A 2.