The accompanying data resulted from a 23 experiment with three replications per combination of treatments designed to study the effects of concentration of detergent (A), concentration of sodiumcarbonate (B), and concentration of sodium carboxymethyl cellulose (C) on the cleaning ability of a solution in washing tests (a larger number indicates better cleaning ability than a smallernumber).Factor LevelsA12ACY AC12121211B с Condition(1)ababсacbcabc=112211111212222 2(a) After obtaining cell totals Xijk. compute estimates of ₁, YAC11, and yAC 21. (Round your answers to two decimal places.)B₁ =unitsunitsunits(b) Use the cell totals along with Yates's method to compute the effect contrasts and sums of squares. (Round your answers to two decimal places.)(contrast)224TreatmentConditionObservations106, 93, 116199, 200, 214197, 202, 185329, 331, 307149, 169, 136243, 247, 220255, 234, 252383, 360, 364(1) = X111.a=X211.b = x121.ab=X221.C = X112ac X212.EffectContrastSS=Ibc=X122.abc = X222.Construct an ANOVA table. (Round your answers to two decimal places.) Construct an ANOVA table. (Round your answers to two decimal places.)Source dfABсABACBCABCErrorTotalSSTest all appropriate hypotheses using a = 0.05. Find the critical value. (Round your answer to two decimal places.)F12Which main effects are significant at level 0.05? (Select all that apply.)A (detergent)OB (sodium carbonate)C (sodium carboxymethyl cellulose)There are no significant factors at level 0.05.Which interactions are significant at level 0.05? (Select all that apply.)AB (detergent and sodium carbonate)AC (detergent and sodium carboxymethyl cellulose)BC (sodium carbonate and sodium carboxymethyl cellulose)ABC (detergent, sodium carbonate, and sodium carboxymethyl cellulose)There are no significant interactions at level 0.05.ConditionMSd(c) Suppose a low water temperature has been used to obtain the data. The entire experiment is then repeated with a higher water temperature to obtain the following data. Use Yates's algorithmon the entire set of 48 observations to obtain the sums of squares and ANOVA table, and then test appropriate hypotheses at level 0.05. (Round your answers to two decimal places.)Observations144, 154, 1582 Rounding Numbers Calculator

Factors Level ABCConditionObservations111(1)106, 93, 116211a199, 200, 214121b197, 202, 185221ab329,…

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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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In a two-factor experiment with two levels of factor A and two levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others. What result(s) would be produced by this pattern of treatment means? a. a main effect for factor A b. a main effect for factor B c. an interaction between A and B d. main effects for both A and B, and an interaction
In a research study to test a new drug on patients with brain cancer, patients were divided into 2 groups randomly. One group received the drug and the other group did not receive the drug. After 6 weeks, the measured results showed reduction in symptoms among the first group who received the drug. Is this an example of an observational study or experimental study? If it is an experiment, what is the controlled factor?
A lamp manufacturer company tests the two new models of LED spotlights for commercial use, trying to decide between 2 models.At the moment the useful life tests are carried out as shown in the table.Perform a two-factor LSD discrimination process with an error of 5%
A survey was conducted to assess the preference of people to reopen LA economy after the extended lockdown due to Corona. Out of 340 males questioned 230 wanted to open the economy and 110 did not. Out of 290 females questioned 218 wanted to open the economy and 72 did not. Can we say that the two factors, gender and preference to open the economy, are related? Use alpha = .05.
Suppose they conducted another set of experiment with increased sample size and saw that the three caffeine concentrations resulted to a different mean adenine concentration. Table below showed summary of Tukey’s HSD. Summarize the result of Tukey’s HSD in Table 2 and provide synthesis, given 5% level of significance. Table 1. Matrix of HSD’s test result for the experiment Treatments Mean difference p - value 0mM – 5mM 2.6283 <0.001 *** 0mM – 10mM 3.9383 0.0112 * 5mM – 10mM 1.3100 0.2458 Table 2. Summary of HSD’s result Treatment Mean SD Summary (in letter or in dot form) 0mM 6.0233 1.1508026 5mM 3.3950 1.8064855 10mM 2.0850 0.9490153 Synthesis: ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________
How to determine the row rank and nullity of the SPL as attached example?
A research has been conducted to determine the factors affecting the tax return preparation period. Accordingly, Y = b0 + b1x1 + b2x2 + b3x3 + b4x4+ ε model containing 4 independent variables was created. 40 accountants were interviewed and the following results were reached: y = 17,2 + 3,8x1 – 1,04x2 + 2,15x3 + 15,1x4 y : Tax filing preparation time (minutes) x1: Income of individuals ($ 1000) x2: Age of individuals x3: Number of people living in the household x4: 1 if individuals are hosts, 0 if not = 5.3, = 0.13, = 0.33, = 1.51, = 4.7, R2 = 0.45. a) Interpret the estimate ? b) interpret the value of R2 c) Whether the coefficient of ?4 is different from 0, by creating the relevant hypotheses, testing at the level of α = 0.01 significance Please. Interpret the results d) Test the zero hypothesis, expressed as ?1 = ?2 = ?3 = ?4 = 0, at the level of significance α = 0.01. Interpret the results
A research has been conducted to determine the factors affecting the tax return preparation period. Accordingly, Y = b0 + b1x1 + b2x2 + b3x3 + b4x4+ ε model containing 4 independent variables was created. 40 accountants were interviewed and the following results were reached: y = 17,2 + 3,8x1 – 1,04x2 + 2,15x3 + 15,1x4 y : Tax filing preparation time (minutes) x1: Income of individuals ($ 1000) x2: Age of individuals x3: Number of people living in the household x4: 1 if individuals are hosts, 0 if not = 5.3, = 0.13, = 0.33, = 1.51, = 4.7, R2 = 0.45. d) Test the zero hypothesis, expressed as b1 = b2 = b3 = b4 = 0, at the level of significance α = 0.01. Interpret the results? already a expert solved first three part can you help me with D
A certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ? 3(2.7)−7(4.2)=−21.33(2.7)−7(4.2)=−21.3 A 3−7=−43−7=−4 B 2.7−4.2=−1.52.7−4.2=−1.5 C…
A researcher conducted a 2-factor ANOVA on the data from his experiment and found a significant main effect of Factor A and a significant main effect of Factor B. Based on this information, what can he conclude about the interaction effect of Factor A & Factor B?
An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use alpha=.05. Factor A is method of loading and unloading; Factor B is the type of ride. Type of Ride Roller Coaster Screaming Demon Long Flume Method 1 46 52 48 48 44 44 Method 2 47 46 52 49 42 48 Set up the ANOVA table (to whole number, but p-value to 2 decimals and F value to 1 decimal, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square -value Factor A Factor B Interaction…
And conduct a two-factor ANOVA to investigate the effects of gender (The name of the variable in SPSS is "gender" and it has two levels, "male" vs. "female") and "minority classification" (In SPSS, the name of the variable is "minority", its label is "Minority Classification" ,and it has two levels "yes" and "no"; referring to whether an individual is part of a minority or not ) on beginning salary (In SPSS the name of the variable is "salbegin", and its label is "Beginning Salary). Use α = .05 a. If the main effect of Minority Classification is significant, describe the main effect of Minority Classification. Include the overall means and corresponding standard deviations in your description. Example = If there is a main effect of maternal diet, is the main effect of maternal diet significant? Why? Provide F-statistic, df of numerator, df of denominator, and p- value? Yes, the main effect of maternal diet is significant because p is less than alpha, F(1,16) = 40.67, p = .0001

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