The accompanying table presents data on yields relating to resistance to stain for three materials (M1, M2 , and M3) treated with four chemicals in a ran- domized block design. (A low value indicates good stain resistance.) Material Chemical M1 M2 M3 Total A 7 21 B 3 4 15 C 8 13 9. 30 D 4 6 8 18 Total 20 36 28 84 (i) Construct an analysis-of-variance table. (ii) Test at the 0.05 level whether mean stain resistance for each chemical is the same. (ii) Test at the 0.05 level whether the stain resistance for each materialt is the same.
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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 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 group of third grade students is taught using a new curiculum. A control group of third grade students is taught using the old curriculum. The reading test scores for the two groups are shown in the back-to-back stem-and-leaf plot. At a = 0.01, is there enough evidence to support the claim that the 8766541160022246 66677 new method reading test scores than the old method does? Assume the population variances are equal. Complete parts (a) through (e) below. Assume the samples are random and independent, and the populations are normally distributed. Old New Curriculum Curriculum 4|3 6 3 40 54443200 589 7 23347789 878 Key: 4|7|0 = 74 Old and 70 New teaching reading produces higher (a) Identify the claim and state H, and H. Which is the correct claim below? O A. "The new method of teaching reading produces equal reading test scores as the old method." OB. "The new method of teaching reading produces higher reading test scores than the old method." O C. "The new method of teaching reading…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 methodThe variability in the amounts of impurities present in a batch of chemical used for a particular process depends on the length of time the process is in operation. A manufacturer using two production lines, 1 and 2, has made a slight adjustment to line 2, hoping to reduce the variability as well as the average amount of impurities in the chemical. Samples of 25 and 25 measurements from the two batches yield 1.04, respectively 0.51 variances. Do the data present sufficient evidence to indicate that the process variability is less for line 2? Use 5% significance level. Conduct a hypothesis test of the airline executive’s belief. [α = 0.05]
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- Various 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.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?A manufacturer of a computer system is interested in improving its customer support services. As a first step its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system failures. Over a period of six months, customers were surveyed and the amount of downtime (in minutes) due to system failures they had experienced during the previous month was collected. The average downtime was found to be 25.09 min and a variance of 144. If it can be assumed that downtime is normally distributed. Obtain a bound above 10% of the downtime of all the customers.