4-3) Group Velocity of ZnSe. Using the Sellmeier coefficients in the formula below, calculate the following properties of ZnSe at 20 = 0.550 μm. I (a) The refractive index n; (b) The phase velocity in m/s; (c) The group velocity in m/s; (d) The group index N. n² = 1+ + 4.45814-202 22-(0.200860) 2,2-(0.391371)2 2,2-(47.1362)² 0.467216.202 2.89566-202 + (λ, in μm)
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- The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.Emenyi Company Limited is considering using Markov analysis to analyze brand switching between three different brands of its Detox medicated soap; Detox White, Detox Green and Detox Orange. The company’s marketing specialist conducted a survey and gathered data which she utilized to estimate the following transition matrix. The matrix shows the probability of moving between brands each month: From White Green OrangeWhite 0.78 0.11 0.11 Green 0.04 0.94 0.02 Orange 0.20 0.04 0.76 The current (month 1) market shares are 50%, 20% and 30% for Detox White, Detox Green and Detox Orange respectively. Required (i) What will be the expected market shares for each of the three brands after two months have elapsed (that is, in month 3)?(ii) What is the long-run prediction for the expected market share for each of the three brands?
- Elon Corporation manufactures parts for an aircraft com-pany. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has adesign (nominal) target of 1.275 inches with tolerancesof 0.024 inch. The CNC process that manufacturesthese parts has a mean of 1.281 inches and a standarddeviation of 0.008 inch. Compute the process capabilityratio and process capability index, and comment onthe overall capability of the process to meet the designspecifications.hw3q3hw3q4
- Bo Using data from 50 workers, a researcher estimates Wage = ẞe + B₁Education + B2Experience + B3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. Intercept Education Experience Age Coefficients Standard Error t Stat p-Value 7.17 4.26 1.68 0.0991 1.81 0.35 5.17 0.0000 0.45 0.10 4.50 0.0000 -0.01 0.06 -0.17 0.8684 a-1. Interpret the point estimate for ẞ1. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour, holding Age and Experience constant. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour, holding Age and Experience constant. a-2. Interpret the point estimate for $2. As Experience…The following data was recorded while observing the increase in the number of butterflies in two different ponds, Pond A and Pond B. Number of Butterflies Present Over 5 Years Year Pond A Pond B 0 50 65 85 1 2 3 4 5 100 O 110 121 133 146 161 110 143 186 What is the rate of growth, r, for each pond and which pond has the fastest average rate of growth over the five years? TA = 1.1, TB = 1.3, mg = 3.72 butterflies/yr TA=0.9, TB=0.8, mg = 3.72 butterflies/yr TA=0.9, TB=0.8, mg=27.2 butterflies/yr TA = 1.1, TB = 1.3, mg=27.2 butterflies/yrWebster Chemical’s nominal weight for filling tubes of caulk is 8.00 ounces ± 0.60 ounces. The target process capability ratio is 1.33. The current distribution of the filling process is centered on 8.054 ounces with a standard deviation of 0.192 ounces. Compute the process capability ratios Cp and Cpk to assess whether the filling process is capable and set properly.
- Elon Corporation manufactures parts for an aircraft company. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has a design (nominal) target of 1.275 inches with tolerances of ±0.024 inch. The CNC process that manufactures these parts has a mean of 1.281 inches and a standard deviation of 0.008 inch. Which of the following statements is true concerning the process capability ratio and process capability index? O The process is off center and incapable. O The process is centered, but incapable. The process is capable and centered. O The process is capable, but off center.Bill Kime's bowling ball factory makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.39 pounds. Each day for 24 days, the average weight, in pounds, of 9 of the bowling balls produced that day has been assessed as follows Day 1 2 3 4 5 6 Average (lb) 9.9 9.9 10.1 10.1 99 99 Day 7 8 9 10 11 12 Average (lb) Day Average (b) 13 14 15 16 17 18 10.1 10.0 10.0 10.1 10.1 10.0 9.9 10.1 10.1 10.0 10.1 10.1 Day 19 20 21 22 23 24 Average (lb) 99 10.0 10.1 9.9 10.0 10.0 a) Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean What are the values of the control limits? Upper Control Limit (UCL)=b (Round your response to two decimal places).A 45 kW rated solar power system has its power output and the Solar irradiance on the PV system measured during daylight hours over a day. Based on the following data, create a scatter plot of the power output of the PV system vs the solar irradiance and comment on the relationship between the two. Based on the data, can you tell which season this day was in? Solar Irradiance on the PV system (kW/m²) 0 0.079 0.333 0.571 0.751 0.86 0.914 0.93 0.904 0.803 0.606 0.345 0.054 Power output from the PV system (kW) 0 3.098 12.438 20.124 25.703 28.498 29.587 29.69 28.798 26.264 20.434 12.223 2