Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in an article.

Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in an article.

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...

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Fiber Density. In the article “Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy” (American Industrial Hygiene Association Journal, Vol. 63, pp. 756–761), I. Moa et al. reported on determining fiber density by two different methods. The fiber density of 10 samples with varying fiber density was obtained by using both an eyepiece method and a TV-screen method. A hypothesis test is to be performed to decide whether, on average, the eyepiece method gives a greater fiber density reading than the TV-screen method. a. identify the variable. b. identify the two populations. c. identify the pairs. d. identify the paired-difference variable. e. determine the null and alternative hypotheses. f. classify the hypothesis test as two tailed, left tailed, or right tailed.
Consider a simple linear regression with the following results: Sample size:24 Estimated slope parameter:B1 = 0.31 Estimated standard error: 0.082 i. Test the following hypothesis with 5% significance level Но : В1 — 0 На : В +0 ii. Test the following hypothesis with 5% significance level Но : В — 0 На: В1 > 0 iii. Test the following hypothesis with 5% significance level. Show the rejection region in a graph. Ho : B1 = 0 На: В1 <0 iv. Test the following hypothesis with 5% significance level. Show the rejection region in a graph. Но : В — 0.5 HA : B1 7 0.5 v. Construct a 95% interval estimate of the slope parameter.
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r=0.543, n=25 O A. Critical values: r = ±0.396, no significant linear correlation OB. Critical values: r = ±0.487, significant linear correlation OC. Critical values: r = ±0.487, no significant linear correlation OD. Critical values: r = ±0.396, significant linear correlation
Question 2: A study of the properties of metal plate-connected trusses used for roof support yielded 35 observations on axial-stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 inches. Use the given output from an analysis of variance with a = 0.01 to answer (a) and(b). Let 'pl.4' denote a plate length of 4 inches, similarly for the other lengths. Df Sum Sq Mean Sq F value Pr (>F) 4 43993 10998 10.48 1.96e-05 *** 1049 0 ***' 0.001 '**' 0.01 0.05 '.' 0.1 ' group Residuals 30 31475 Signif. codes: (a) (b) Tukey multiple comparisons of means 99% family-wise confidence level Fit: aov (formula p adj $group diff 1wr upr pl.12-pl.10 29.814286 -31.98149 91.610065 0.4363237 pl.4-pl.10 -74.142857 -135.93864 -12.347078 0.0015294 pl. 6-pl.10 -39.300000 -101.09578 22.495779 0.1827394 pl. 8-pl.10 -32.228571 -94.02435 29.567208 0.3591363 pl.4-pl.12 -103.957143 -165.75292 -42.161364 0.0000130 pl.6-pl.12 pl. 8-pl.12 pl.6-p1.4 pl.8-pl.4 1 pl. 8-pl.6 -69.114286 -130.91006 -7.318507 0.0033328…
Calculate the average values of the Cp and Cpk capabil-ity indices for the BOD data , assuming that LSL=5 mg/L and USL=35 mg/L. Do these val-ues of the indices indicate that the process performance is satisfactory?
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A company manufactures an electrical cooling fan. When the fans are performing properly, samples of 200 fans average 12.5 watts with an average range of 1.2 watts. A 3σ control chart program is being used to monitor the performance of the fans, and these data from the 10 most recent samples were collected: Sample Number Sample Mean Sample Range 1 12.5 1.1 2 12.45 1.2 3 12.55 0.9 4 12.50 0.8 5 12.45 0.9 6 12.60 1.0 7 12.48 1.4 8 12.46 1.1 9 12.56 0.9 10 12.48 0.8 Compute the 3σ control limits and center line for an ⁻x chart. Compute the 3σ control limits and center line for an R chart. Plot the sample data on the ⁻x and R charts and decide if the performance of the fan is in control.
16.17 In an experiment comparing four diets (treatments), the weight gain y (pounds per day) of pigs was recorded along with two covariates, initial age x₁ (days) and initial weight x2 (pounds). The data are presented in Table 16.11. (a) Using (16.67), (16.68), and (16.69), find Ex, exy, and eyy. Find B. (b) Using (16.77), (16.81), and (16.82), find SSEyr, SST.x, and SS(alu, B). Then test Ho: a₁ = ₂ = a3 = a4, adjusted for the covariates, using the F statistic in (16.83). (c) Test Ho: B = 0 using (16.84). (d) Find B₁, B₂, B3, and 4 using (16.88). Find SSE(F), and SSE(R)y.x using (16.86) and (16.87). Test Ho: B₁ B₂ B3 B4 using (16.89). X1 X2 y X1 78 61 1.40 78 90 59 1.79 99 94 76 1.72 80 71 50 1.47 75 1.26 94 1.28 91 1.34 75 1.55 63 1.57 62 1.26 TABLE 16.11 Initial Age x₁, Initial Weight x2, and Rate of Gain y of 40 Pigs Treatment 1. Treatment 2 Treatment 3 Treatment 4 99 61 80 54 83 57 75 45 62 41 67 40 X2 y X1 74 1.61 78 75 1.31 83 64 1.12 79 48 1.35 70 1.29 85 1.24 83 1.29 1.43 1.29…
Question 3 Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.197, n = 15 Critical values:r= +0.514, no significant linear correlation Critical values: r= +0.532, no significant linear correlation Critical values: r= ±0.514, significant linear correlation Critical values: r 0.514, no significant linear correlation
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…
Determine the following ; Conclusion HYPOTHESIS Calculation
The titanium content of steel is determined in two laboratories by means of atomic absorptionspectrometry. The following data were obtained: Lab 1 0.470 0.484 0.463 0.449 0.482 0.454 0.477 0.409 Lab 2 0.529 0.490 0.489 0.512 0.486 0.502 - - A. Determine the variance of the measurement data obtained in the two laboratories.B. Is there any significant difference between these variances?