The cetane number is a critical property in specifying the ignition quality of a fuel used in a diesel engine. Determination of this number for a biodiesel fuel is expensive and time- consuming. The article “Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil. The article's authors fit the simple linear regression model to this data, so let s does the same. 132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0 y 46.0 48.0 51.0 52.1 54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0 51.4 3) Estimate the correlation coefficient (Pearson coefficient), r, between x and y and explain briefly the strength of r and its direction and comment the p-value. 4) Construct a 95% two-sided confidence interval for the regression line.

The cetane number is a critical property in specifying the ignition quality of a fuel used in a diesel engine. Determination of this number for a biodiesel fuel is expensive and time- consuming. The article “Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil. The article's authors fit the simple linear regression model to this data, so let s does the same. 132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0 y 46.0 48.0 51.0 52.1 54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0 51.4 3) Estimate the correlation coefficient (Pearson coefficient), r, between x and y and explain briefly the strength of r and its direction and comment the p-value. 4) Construct a 95% two-sided confidence interval for the regression line.

Name: The cetane number is a critical property in specifying the ignition q
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: The cetane number is a critical property in specifying the ignition quality of a fuel used in adiesel engine. Determination of this number for a biodiesel fuel is expensive and time-consuming. The article "Relating the Cetane Number of Biodiesel Fue

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

The Specific Absorption Rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user's body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.5 watts per kilogram. A sample of 47 models was tested and the average of their Specific Absorption Rates (SARs) was found to be 1.18 watts per kilogram. Assume that the population standard deviation is 0.25 watts per kilogram. Construct a 90% confidence interval for the mean of the SARs for cell phones that received certification from FCC. Confidence interval:( , ) Interpretation: We are % confident that the mean of the SARs for cell phones that received certification from FCC is between watts per kilogram and watts per kilogram.
Show complete solution and explain the steps in answering.
“Passive and Active Smoke” in Appendix B includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, Mean = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, Mean = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. 1. Construct a confidence interval estimate of the difference betwen the mean continen levels fo the two groups of nonsmokers. What confidence level would be appropriate? 2. Find the margin of error E using the formula. 3. What is the confidence interval? Explain the meaning of the confidence interal and what the limit represents.
4. Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the accompanying table (based on data from “Essential Hypertension: Effect of an Oral Inhibitor of Angiotensin-Converting Enzyme”, by MacGregor et al., BMJ, Vol. 2). Using a 0.01 significance level, is there sufficient evidence to support the claim that captopril has an effect on systolic blood pressure? Explain why statistical methods from Z-interval, Z-test, T-interval or T-test –cannot be used for this problem. Then, use the sign test to conduct the required test in R studio. Please show your work.
Chlorophylls a and b are plant pigments that absorb sunlight and transfer the energy into photosynthesis of carbohydrates from CO2 and H2O, releasing O2 in the process. Chlorophylls were extracted from chopped up grass and measured by spectrophotometry. The table shows results for chlorophyll a for four separate analysis of five blades of grass. Chlorophyll a (g/L) Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 1.09 1.26 1.1 1.23 0.85 0.86 0.96 1.21 1.3 0.65 0.93 0.8 1.27 0.97 0.86 0.99 0.73 1.12 0.97 1.03 Four replicate measurements for each blade of grass tell us the precision of the analytical procedure (sanalysis). Differences between mean values for each of the five blades of grass are a measure of variation due to sampling (ssampling). Using Excel and it’s ANOVA function, find the standard deviations attributable to sampling and to analysis, as well as the overall standard deviation arising from both sources.
The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. 1. For what value of z does exactly 95% of the area under a Gaussian curve lie between ± z? Use this multiplier to find the range of measured cholesterol concentrations that would include 95% of the trials from the “parent population” (μ and σ) given above. 2. Calculate z for a trial in which the measured total cholesterol concentration is 6.302 mmol/L. 3. What is the probability that a trial will give a cholesterol…
Mist (airborne droplets or aerosols) is generated when metal- removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The article "Variables Affecting Mist Generaton from Metal Removal Fluids" (Lubrication Engr., 2002: 10-17) gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 μm (mg/m³): x y 89 177 189 354 362 442 965 .40 .60 .48 .66 .61 .69 .99 a. The investigators performed a simple linear regres- sion analysis to relate the two variables. Does a scat- terplot of the data support this strategy? b. What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? c. The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a…
Answers: 1.a) rXY = 0.461, t = 1.272, Do not reject H0: no evidence for a significant correlation between the two variables b) 43.66
2. To investigate the effect of pH and catalyst concentration on product viscosity (sSt). Two levels of pH were used 5.6 and 5.9 and two catalyst concentration 2.5 and 2.7. Four products were tested with each combination of pH and catalyst. a. Use the estimate table below to test for main effects and interaction using a = 0.05. What are your conclusions? Predictor Constant Coefficient SDCoeff 191.563 165.49 pH 2.937 1.158 2.52 Catalyst -0.062 1.158 -0.05 pH*Catalyst 5.812 1.158 5.02 b. What is the value for the overall average viscosity? c. Write the regression model for this experiment. d. Below the interaction plot for the experiment. Discuss the information provided by the plot. To maximize viscosity what would be the recommended setting? Interaction Plot for Viscosity Data Mears 200 195 190- 185 Catalyst Concentration Mean Product Viscosity (cSt)
widely used as dielectrics and coolants in electrical systems in the past. They were found to be a major environmental contaminant in the 1960s. In a study, the mean PCB content at each of thirteen sites was reported for the years 1982 and 1996 (from “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data”, Journal of Great Lakes Research 24 (1): 12-31, 1998). The data are below.Site:12345678910111213198261.4864.4745.5059.7058.8175.9671.5738.0630.5139.7029.7866.8963.93199613.9918.2611.2810.0221.0017.3628.207.3012.809.4112.6316.8322.74(a) Which test would be more appropriate in this case: a t-test for the difference between two population means, or a paired t-test? Why?(b) Do the data provide sufficient evidence to support the claim that the mean PCB level has decreased in the region? Be sure to check all assumptions, write the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value,…
Lecture(8.8): The amount of time people engage in physical activity mat be related to health outcome. Those who report that they spend more than 15 hours are put into one while those who spend less 10 were put into another group. (Those who fall in between 10 and 15 were left out of the study); The reaearcher then ask the participants to wear a monitor for one month. The average time in minutes is recorded and shown below . Is there any evidence that on average people who watch less than 10 hours watching televsion spend more time on physical activity.?. Test the hypotheses at (alpha=0.05) using the 5 step procedure <10 hours 75 63 118 35 82 >15 hours 62 6 78 43 22 33
The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"† compared two different instruments for measuring a person's ability to breathe out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. Subject Mini-WrightMeter WrightMeter Subject Mini-WrightMeter WrightMeter 1 512 494 10 445 433 2 430 395 11 432 417 3 520 516 12 626 656 4 428 434 13 260 267 5 500 476 14 477 478 6 600 557 15 259 178 7 364 413 16 350 423 8 380 442 17 451 427 9 658 650 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce…