7. A paper in Quality Engineering [2013, Vol. 25(1)] presented data on cycles to failure of solder joints at different temperatures for different types of printed circuit boards (PCB). Failure data for two temperatures (20 and 60°C) for a coppernickel-gold PCB follow. 20°C 218, 265, 279, 282, 336, 469, 496, 507, 685, 685 60 C 185, 242, 254, 280, 305, 353, 381, 504, 556, 697 a. Test the null hypothesis at a = 0.05 that the cycles to failure are the same at both temperatures. Is the alternative one or two sided? b. Find a 95% confidence interval for the difference in the mean cycles to failure for the two temperatures.
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- 5. Oxygen demand is a term blologists use to describe the axygen needed by fish and other aquatic organisms for survval. The Environmental Protection Agency conducted a study of a wetland area in Marin County, Californla. In this wetland environment, the mean oxygen demand was u=9.9 mg/L, and a= 1.7 mg/L. (Reference: EPA Report 832-R- 93- 005). Let x be a random varlable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. a. An oxygen demand below 8 mg/L Indicates that some organisms In the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? b. A high oxygen demand can also indicate trouble. An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L?7. A paper in Quality Engineering [2013, Vol. 25(1)] presented data on cycles to failure of solder joints at different temperatures for different types of printed circuit boards (PCB). Failure data for two temperatures (20 and 60°C) for a coppernickel-gold PCB follow. 20°C 218, 265, 279, 282, 336, 469, 496, 507, 685, 685 60°C 185, 242, 254, 280, 305, 353, 381, 504, 556, 697 a. Test the null hypothesis at x = 0.05 that the cycles to failure are the same at both temperatures. Is the alternative one or two sided? b. Find a 95% confidence interval for the difference in the mean cycles to failure for the two temperatures.3. You are curious to understand if there is a relationship between the average grade (in %) that students received in Assignment 1, 2, and 3 of ECOR 2050 (assignments that covered midterm material) and their grade (in %) in the Midterm of the course. You are limited to collect 7 sets of data (midterm vs average assignments). For that, you can check the google sheets to find grades of assignment 1, 2, and 3 and midterm for 7 students. You should be careful that your data set is not biased. a) Collect the information and record them in the table below (please use a typed table/numbers as we need to copy/paste your numbers into Excel for checking your solution and marking). Mention how you ensured that your data set is random and unbiased. Student 2 3 4 6. 7 Grade (%) Average of Assignment 1, 2, and 3 (assignments before midterm) Midterm b) Using the collected information, conduct a simple linear regression analysis and find the regression line. Also, estimate the coefficient of…
- 3) Fresh tomatoes were stored at 15°C. Lycopene (orange-red pigment) contents were determined for a period of 10 weeks at 15°C. The results are presented in Table 3. Lycopene degradation during storage of tomatoes is known to give the straight line in a semi-log graphic paper. Table 3– Lycopene contents in fresh tomatoes stored at 15°C Storage time (week) Lycopene content (mg/kg) 33 2 23 6 5.3 10 2.1 Find out the lycopene concentration in tomatoes after 4 months of storage at 15°C. Note: Give units wherever it is applicable!!!! Σxy- (Σx Σy / ) ΣyΣx?- Σx Σxy Ex² - [ (Ex)² / n) ] n (E x² - [ (Ex)² / n) ] )3) Fresh tomatoes were stored at 15°C. Lycopene (orange-red pigment) contents were determined for a period of 10 weeks at 15°C. The results are presented in Table 3. Lycopene degradation during storage of tomatoes is known to give the straight line in a semi-log graphic paper. Table 3- Lycopene contents in fresh tomatoes stored at 15°C Storage time (week) Lycopene content (mg/kg) 33 2 23 6 5.3 10 2.1 a) Find out the equation describing the degradation of lycopene in tomatoes at 15°C, using the "linear regression analysis. Note: Give units wherever it is applicable!!!! Σxy- (Σx Σy / n ) ΣyΣx%- Σx Σxy b = Ex² - [ (Ex)² / n) ] η (Σχ'- [ (Σx)>/ n) ] )Environmental conditions can affect the growth of coral. To study this, a researcher examined a species of coral that is found in the Caribbean Sea and the Gulf of Mexico. At 12 localities, he determined the average annual calcification rate of coral over a period of several years and the average annual maximum sea surface temperature during the same period. Calcification rate affects the growth of coral, with higher rates corresponding to greater growth. The table contains data for these 12 localities. Maximum sea surface temperature (°C) and calcification rate (g cm² yr¯¹) Maximum Sea Surface Temperature 29.4 29.4 29.4 29.6 29.1 28.7 Calcification Rate 1.48 1.53 1.52 1.48 1.31 1.25 Maximum Sea Surface Temperature 29.7 29.5 29.4 29.0 29.0 29.0 Calcification Rate 1.63 1.53 1.46 1.24 1.29 1.12 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 CrunchIt! The residuals for average annual maximum sea surface…
- Data from the US Department of Energy’s US Energy Information Administration (eia.doe.gov) provides a look at the energy-related carbon dioxide emissions by end use sector (residential, commercial, industrial, transportation) from years 1990 to 2009. (Report # DOE/EIA0573(2009)). Here we would like to see if the CO2 emissions from the Industrial sector are less than that from the Transportation sector. Below are the results: 14. What type of study is this? a. Paired b. Two-Sample Independent 15. What type of plot would we use? a. Histogram of the differences b. Side-by-side boxplots c. Pie chart d. Bar graph 16. Was the HOV/pooled test used above (hint: look at the df)? YES NO 17. Is there evidence that the CO2 emissions from the Industrial sector are less than that from the Transportation sector? YES NO 18. If we were to test to see if there was a difference between the CO2 emissions from the Industrial sector and the Transportation sector, what would be the p-value? (report to 3…An article in Urban Ecosystems, "Urbanization and Warming of Phoenix (Arizona, USA): Impacts, Feedbacks and Mitigation" (2002, Vol. 6, pp. 183-203), mentions that Phoenix is ideal to study the effects of an urban heat island because it has grown from a population of 300,000 to approximately 3 million over the last 50 years and this is a period with a continuous, detailed climate record. The 50-year averages of the mean annual temperatures at eight sites in Phoenix are shown below. Check the assumption of normality in the population with a probability plot. Construct a 90% confidence interval for the standard deviation over the sites of the mean annual temperatures. Site Sky Harbor Airport 23.3 Phoenix Greenway 21.7 Phoenix Encanto 21.6 Waddell Litchfield Laveen Average Mean Temperature (°C) Maricopa Harlquahala i 21.7 21.3 20.7 20.9 20.1 Round the answers to three decimal places. sosiThe 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 Ho: Md = 0 Ha: Ha 0 = 0 Ho: Md < 0 Ha: Md P-value = X-ray 4.75 7.00 9.25 12.00 5 17.25 6 29.50 7 5.50 8 6.00 9 8.00 10 8.50 11 9.25 12 11.00 13 12.00 14 14.00 15 17.00 16 18.00 = 0 1 2 3 4 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 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 = 0.534 0.000 X X State the conclusion in the problem context. We fail to reiect H.…
- 10.63) In material sciences, measuring temperatures accurately is of great importance. Optical pyrometry is an established method used for measuring temperatures. These pyrometric temperature measurements are affected by the selection of operating wavelength and atmospheric conditions. To solve some of the measurement problems, Rohner and Newmann developed a new system based on UV-B (ultraviolet) wavelength range for pyrometry and tested it on a blackbody without solar irradiation. They recorded the percentage of deviation of the UV temperatures from the blackbody temperatures. Two sets of data were collected; one based on the calibration at 1400 degrees C and the other at 1500 degrees C. The data are shown in the attached image. Is the mean percent deviation significantly higher at 1500 degrees C? Use α = 0.05.The 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.)2. The 2 data sets are replicates of pH values of an alkaline solution (set A) and acidic solution (set B). (1) which is more precise? (2) which is more accurate? 11.2, 10.7, 10.9, 11.3, 11.5, 10.5, 10.8, 11.1, 11.2, 11.0 (x, = 10.7) B) 5.2, 6.0, 5.2, 5.9, 6.1, 5.5, 5.8, 5.7, 5-7, 6.o (x = 5.8) %3D