IE 590 Summer 2024 Homework 1 Before attempting Homework 1: s View Lectures 1-2 + Read the textbook. Introduction to Design of Experiments. Donglas C. Montgomery. Chapters 2-5. Please let me know if vou have questions. L Solve the following problems (Using Minitab). The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.00015 in. A random sample of 20 rods has an average diameter of 0.5053 in. (a) Test the hypothesis that mean rod diameter is 0.5045 in. Assume a two-sided alternative and use a=0.05. (b) Construct a 95% two-sided confidence interval on the mean rod diameter. The number of flaws in a fibre optic cable follows a Poisson distribution. The average number of flaws in 100m of cable is 1.8. a) What is the probability of exactly three flaws in 250m of cable? b) What is the probability of at least two flaws in 150m of cable? It is known that 0.7% of the circuit boards from a production line are defective. If a random sample of 220 circuit boards is taken from this production line, use the Poisson approximation to estimate the probability that the sample contains: a) Exactly 10 defective boards. b) Atleast 3 defective boards. The output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at random on voltage are as follows: 10.35, 5.30, 10.00, 5.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 5.25, 9.38, and 10.85. (a) Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using a=0.05. (b} Construct a 95% two-sided confidence interval on . IE 590 Summer 2024 Homework 1 5. Suppose we have a turning operation in a process where we are manufacturing pins to a diameter of 125 +/- 005 inches. We have five different machines making the same part and we take five random samiples from each machine to obtain the following diameter data: a} From the analysis of these data can we conclude that the factor "machine\" has an effect with a=0.057 Check assumptions. b) If we have a significant difference use Fisher's method to evaluate the differences, and use the same level of significance. Write all the necessary outputs to answer the questions. 6. Theinterest was focused on the potential differences between the designs of nozzles, with speed considered a disturbing variable. The data is presented below Flow Rate Velocity Nozzle Design 1173 1437 16.59 \" 28.74 75 0.81 0.75 0.77 0.78 0 a) Does the nozzle design affect the shape factor? Compare the nozzles with a scatter plot and analysis of variance, using a = 0.05. by Amnalyze the residuals from this experiment