Problem 1 Consider the hypothesis test Ho: [11 = [12 against H: u] at [12. Suppose that sample sizes m = 10 and n: = 15 and: sample means 4.7and 4.7 and sample standard deviations of 10 and 5. Cl = 0.05. 1. Test the variances: answer the following questions: -What is the test statistics Q)? -What is the Critical value FOL? -are the variances equal or different? 2. Test the population means: answer the following questions: -Ca1culate the test statistics (T)? -What is the Critical value T(a/ 2) (t value from the table? -Are the means equal or different? 3. Calculate the 95% condence interval of (u1-u2). Problem 2 Two machines are used for lling plastic bottles with a net volume of 16.0 ounces. The ll volume can be assumed to be normal with standard. A member of the quality engineering staff suspects that both machines ll to the same mean net volume. A random sample of 10 bottles is taken from the output of each machine. Use Minitab for this exercise and assume the variances are equal. Do you think the engineer is correct? Use a = 0.05. What is the P-value for this test? Write the Ho and H1. What is the pooled variance? What is the test statistic? What is the p-value? Do you think the engineer is correct? 9914'9393!' Calculate a 95% condence interval on the difference in means. Problem 3 Consider the following computer output. Two-Sample T-Test and CI Sample N Mean StRev SE Mean 1 12 10.94 1 . 26 0.36 2 16 12 . 15 1. 99 0. 50 Difference = mu (1) - mu (2) Estimate for difference: -1.210 95% CI for difference: (?, ?) T-test of difference = 0 (vs > 0) : T-value = ? P-value = ? DF = ? Both use Pooled StDey = ? 1. Read the output carefully and Give Ho and Hi 2. Calculate T value. 3. What are your conclusions if a = 0.05? 4. What are your conclusions if a = 0.01? 5. This test was done assuming that the two population variances were equal or different? 6. Estimate with 90% confidence the different in the means.Problem 4 The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random of eight cars and runs the cars until the tires wear out. The data (in kilometers) follow. Is there any difference in mean life of these two brands of tires? Car Brand 1 Brand 2 1 36,925 34,318 2 45,300 42,280 3 36,240 35,500 32,100 31,950 5 37,210 38,015 6 48,360 47,800 38,200 37,810 8 33,500 33,215 1 . Is this samples independent or paired samples? Explain. 2. Write Ho and H1 3. Calculate Test statistics(T). What is the critical value (T from tables)? 5. What is your conclusions if a = 0.05? 6. Estimate with 90% confidence the different in the means. Which brand would you prefer based on this calculation?Problem 5 Consider the hypothesis test Ho: pi = p2 against Hi: pi # pz. Suppose that sample sizes mi = 10 and n2 = 15 and, and X1=4 and X2= 6. a = 0.05. -What is the test statistics ( Z)? -What is the Critical value Z(a/2) (z value from the table)? -Are the two proportions equal or different? -Calculate the 95% confidence interval of (p1-p2)