Methane biofilters can be used to oxidize methane using biological activities. It has become necessary to compare performance of two test columns, A and B. The methane outflow level at the surface, in nondimensional units of X= {50, 100, 150, 200], was detected and is tabulated below against the respective methane inflow into each test column. The following fuzzy sets represent the test columns: A = { B = { 0.7 0.15 0.25 0.5 + 100 150 200 + + 50 a. Union of A and B 0.2 0.3 0.6 0.65 + + + 50 100 150 200 Calculate the union, intersection, and the difference for the test columns. b. Intersection of A and B c. Different between A and B
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- Find the new data point (x,y) in which x=2 from the data points (1,3) and (4,12)A statistical program is recommended. An automobile dealer conducted test to determine whether the time needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data (time in minutes) obtained follow. x₂ Analyzer 0 Computerized Electronic Define all variables. Let x₁ = 0 if a computerized analyzer is used, or let x₁ = X3 O Ho: B₁ * 0 H₂: B₁ = 0 0 Compact 1 52 Car 41 Compact Intermediate Full Size Intermediate O Ho: One or more of the parameters is not equal to zero. H₁: B₂ =B3 = 0 Car 57 Find the p-value. (Round your answer to three decimal places.) p-value = 43 Use α = 0.05 to test for any significant differences between the two analyzers. State the null and alternative hypotheses. O Ho: B₁ = 0 H₂: B₁ = 0 Full Size o Ho: Ba = By = 0 H₂: One or more of the parameters is not…A housewife wanted to know which soil is best for her pechay plants: the soil purchased from an online seller, soil from her backyard compost or the soil underneath the nearby bamboo tree. She planted 30 pechay seeds into each soil source and then compared the growth of pechay after a month. Identify the independent, dependent and extraeous variable.
- The Senator of Azenator State, is worried about the rising numbers in high blood pressure related deaths in his Jurisdiction and wants an end to this canker. A reputable medical research officer has claimed that, the situation is probably as a result of the ageing population of his State. The blood pressures, Y (mmHg), and Ages, X (years) of 10 hospital patients were sampled from Azenator State and summarized below. Patient A B C D E F G H I J Age(X) in Years 20 25 50 30 45 60 10 15 35 70 BP(Y) in (mmHg) 80 85 125 90 100 135 80 70 100 140 NB: Approximate to 2 decimal placesUse the table to answer the questions that follow;i) Calculate the product moment correlation coefficient for the data and interpret your result.ii) If the Senator decides to purchase and distribute Norvasc (a medicine that reduces blood pressure), based on your results in (i), which age group (youth or old adults) should be given priority? Briefly explain your answer. iii) Give a reason to support fitting…A paper company has about 50 paper mills distributed over 3 provinces. Each mill records specified factors that contribute to its profitability. The company has classified the mills as Profitable and Non- Profitable. They recorded paper weight produced as an indicator of profitability. That is, X₁ = PAPER (weight in 10000 kilograms) Y = PROF (1 = profitable and 0 = not profitable) Y Profitable 1 1 0 It was found that Paper 2 1.5 0.8 ît= exp(-2.94 + 0.098X₁) 1 + exp(-2.94 +0.098X₁) 1. Give the fitted logistic response function. 2. Give the fitted logit response function 3. Show that ft loge € (₁^²) = = -2.94 + 0.098X₁ 4. Give the odds to be used of this logistic regression for X₁ = 0.7. Explain your result. 5. What is the estimated probability that a mill be profitable if it produces 7 000 kilograms of paper? 7. Interpret the regression coefficients of ît= Also find the odds ratio for b₁. exp(-2.94 + 0.098X₁) 1 + exp(-2.94 +0.098X₁)During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large. The data in the table show various numbers of seeds planted per square foot and yields (in pounds per square foot) for a sample of fields. A 2-column table with 15 rows. Column 1 is labeled number of seeds (per square foot) with entries 28, 75, 30, 43, 71, 35, 40, 59, 66, 79, 85, 81, 16, 33, 16. Column 2 is labeled yield (pounds per square foot) with entries 131, 171, 132, 166, 169, 150, 161, 183, 173, 161, 147, 157, 86, 145, 86. Which scatterplot represents the seed and yield data? A graph titled number of Seeds and Crop Yield has seeds (per square foot) on the x-axis, and yard (pounds per square foot) on the y-axis. The points curve up to a point, and…
- The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern. The least-squares line is = -964.98 + 8.60x. Because 1 lb = 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y = 0.4536(old y). What is the equation of the least-squares line when y is expressed in kilograms? (Give the answer to two decimal places.) = x 202.9 212.9 222.9 232.9 242.8 y 814.5 786.1 961.2 1118.8 1077.0The authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. The table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete 0 Ho: Md = Ha: Md 0 < 0 5 6 7 8 9 10 11 12 13 14 15 16 X-ray 4.75 7.00 9.25 12.00 17.25 29.50 5.50 6.00 8.00 8.50 9.25 11.00 12.00 14.00 17.00 18.00 USE SALT Ultrasound 4.75 4.00 9.00 11.75 17.00 27.75 6.50 6.75 8.75 9.75 9.50 12.00 12.25 15.75 18.00 18.50 X Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = 0.000 Mx-ray ultrasound.)Burning fuels in power plants and motor vehicles emits carbon dioxide (CO2), which contributes to global warming. The CO2 emissions (metric tons per capita) for countries varies from 0.02 in Burundi to 44.02 in Qatar. Although the data set includes 214 countries, the CO2 emissions of 15 countries are not available on the World Bank database. The data set is too large to display but the data for the first five countries is given. Use the full data set with data on the 214 countries to answer the questions. To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV Crunchlt! Country CO2 Emissions (Metric Tons per Capita) Aruba 23.92 Andorra 5.97 Afghanistan 0.43 Angola 1.35 Albania 1.61 Find the mean and the median for the full data set. Round your answers to three decimal places. The mean for these data is tons per person The median for these data is tons per person
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