5. The following table lists the tensile strengths of a rubber compound produced by three different methods, denoted A, B, and C. Method Tensile Strength S A 4038 4347 3652 4410 3432 4071 4242 3720 4232 В C Compute SSTreatment, SSE, and SST and verify that SST = SSTreatment + SSE.
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- Three adhesives are being analysed for their impact on the bonding strength of paper in a pulp and paper mill. The adhesives are each randomly applied to four batches. The data is shown in Table 2. Here, the three treatments are the adhesives (p=3) and the number of replications for each treatment is 4 (r=4). Is there a difference among the adhesives in terms of the mean bonding strength? Test at the 5% significance level. Given F0.05,2,9 = 4.26 Adhesive Bonding strength (kg) type Adhesive 1 10.2 11.8 Adhesive 2 12.8 14.7 Adhesive 3 7.2 9.8 Table 2 Bonding strength data 9.6 13.3 8.7 12.4 15.4 9.2An experiment was conducted to determine the effect of machining factors on ceramicstrength. Two levels of table speed (slow and fast), two directions (longitudinal and transverse) and two levelsof wheel grit (I and II) were identified by the researcher. The experiment was replicated three times and thestrength of each randomly selected ceramic was obtained. The ANOVA table of the results of the analysis areas follows. 1. Refer to the ANOVA table at a=0.01, what is the conclusion for testing significance in 3-way interaction Reject/Fail to Reject Ho 2. If sequential test of hypothesis is performed the following are (True or False)? a. All 2-way interaction effects are going to be tested b. All main effects are going to be tested 3. What combination of effects will result to a significant result at a=0.01 if should all test are going to be performed among the main effects and two way interactions? (choose 1pair/combination: direction, wheel grit, speed)Determine the kurtosis if the data given is a sample.
- Blood cocaine concentration (mg/L) was determinedboth for a sample of individuals who had died fromcocaine-induced excited delirium (ED) and for a sampleof those who had died from a cocaine overdose withoutexcited delirium; survival time for people in bothgroups was at most 6 hours. The accompanying datawas read from a comparative boxplot in the article“Fatal Excited Delirium Following Cocaine Use” (J.of Forensic Sciences, 1997: 25–31). ED 0 0 0 0 .1 .1 .1 .1 .2 .2 .3 .3.3 .4 .5 .7 .8 1.0 1.5 2.7 2.83.5 4.0 8.9 9.2 11.7 21.0Non-ED 0 0 0 0 0 .1 .1 .1 .1 .2 .2 .2.3 .3 .3 .4 .5 .5 .6 .8 .9 1.01.2 1.4 1.5 1.7 2.0 3.2 3.5 4.14.3 4.8 5.0 5.6 5.9 6.0 6.4 7.98.3 8.7 9.1 9.6 9.9 11.0 11.512.2 12.7 14.0 16.6 17.8 a. Determine the medians, fourths, and fourth spreadsfor the two samples.b. Are there any outliers in either sample? Any extremeoutliers?c. Construct a comparative boxplot, and use it as abasis for comparing and contrasting the ED andnon-ED samples.The mean tensile strengths of 4 different cotton blends (blends 1,2, 3, 4) are being compared using an Analysis of Variance (ANOVA). For each blend, a random sample of s = 20.0, s, = 25.5, s size n = 11 fabric squares is taken. The sample variances are %3D = 24.3, s 30.5. Given that the value of s2 =8.8, calculate the value of the ANOVA test statistic. Enter your answer to two decimal places. Hint: one can check by the definition that the following is true: (1) Treatment of mean squares: MSTrt = n s2. (2) Error of mean squares: M SE = E, s = s + s+ s + s.An experiment was conducted to investigate the variation of chemical Y solubility in water. The amounts in kilograms that dissolved in one liter of water at nine different temperatures were recorded, and the data was analyzed with IBM-SPSS software. Based on the data and IBM-SPSS software output given (refer images): i) Validate that the Pearson correlation coefficient value is 0.984ii) Compute the value of X in Table 2iii) Determine the proportion of variance in the dependent variableiv) Estimate mass that dissolved in the water if the temperature is set at 100C.
- Highway engineers in Ohio are painting white stripes on a highway. The stripes are supposed to be approximately 10 feet long. However, because of the machine, the operator, and the motion of the vehicle carrying the equipment, considerable variation occurs among the stripe lengths. Engineers claim that the variance of stripes should be less than 16 inches squared. At α = .05, use the sample lengths given here from 12 measured stripes (in feet and inches) to test the variance claim. Assume stripe length is normally distributed. (in feet) (in inches) 9.85 118.2 9.7 116.4 9.9 118.8 9.5 114 9.15 109.8 10.1 121.2 10 120 9.8 117.6 9.9 118.8 10.3 123.6 10.1 121.2 10.2 122.4 The appropriate test for this question is: a Z-test for the true variance of stripe length. a t-test for the true mean of stripe length. a Chi-square test…A research study investigated the composition of wines from the Rhine and Moselle wine regionsof Germany. One component measured was the concentration of i-Butyl alcohol. The results ofthe study are listed in the following table:Region n i-Butyl alcohol (mg/100ml)Rhine 9 ̄x =5.32,s =2.24Moselle 14 ̄x =3.62,s =0.97(a) Assume that the underlying population variances from the two regions are identical. At the0.05 level of significance, test the null hypothesis that the mean concentration of i-Butylalcohol is the same for wines from the Rhine and Moselle regions.Construct a 95% confidence interval(b) Now assume that the underlying population variances from the two regions differ. At the 0.05level of significance, test the null hypothesis that the mean concentration of i-Butyl alcohol isthe same for wines from the Rhine and Moselle regions, construct a 95% confidence interval(c) If you were to provide a report to the investigators which of the above results would youinclude and why?Consider a set of data (x₁, yi), i=1,2,..0 and the Simple linear regression equation given by : 4 y₁ = B₁+ B₁²x₁ The /s Standardized random variable of given by 2= B₂₁ - B²₁₂² FSSxx find the mean and the variance of Zo
- 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. (b) the sample variance s2 from the definition [Hint: First subtract 180 from each observation.] (c) the sample standard deviation (d) s2 using the shortcut methodLast school year, the student body of a local university consisted of 35% freshmen, 25% sophomores, 24% juniors, and 16% seniors. A sample of 300 students taken from this year's student body was taken to determine if there had been a significant change in % of students for each classification for this year as compared to last year. This analysis is an example of a Regression O Goodness of Fit Analysis of Variance Test of IndependenceVarious doses of poisonous substance were given to groups of 25 mice and the following results were obtained in Table Q1: Table Q1 Dose (mg) Number of deaths 4 1 6. 3 6. 10 8 12 14 14 16 16 20 (b) Calculate the sample correlation coefficient between the dose and the number of death. Interpret the result. (c) Calculate the value of Sum Squares Error (SSE) and Mean Square Error (MSE). (d) At the 0.05 level of significance, test the slope greater than one.
