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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4.16 Consider an experiment where three coins are tossed. The first coin has a "1" and a "2" marked on its two sides. The second coin has a "2" and a "3" marked on its two sides. The third coin has a "3" and a "4" marked on its two sides. Let X denote the product of the three numbers that are face up. (a) Obtain the pmf of X. (b) Calculate the expected value of X/2.
How a single interpretation is possible for μ1 – μ2?
& The accompanying table gives plasma epinephrine concentration for ten experimental subjects during (1) isoflurane, (2) halothane, and (3) cyclopropane anesthesia ("Sympathoadrenal and Hemodynamic Effects of Isoflurane, Halothane, and Cyclopropane in Dogs." Anesthesiology, 1974: 465-470). a. Does the choice of anesthetic affect true average concentration? Test H: a, = a, = a, = 0 at level .05 after constructing the ANOVA table. %3D Subject (B) 2 3 4 5 .51 1.00 .39 28 .39 29 Anesthetic 38 .21 2 .30 3 1.07 1.35 .63 (A) .69 .28 1.24 6. 7 8 10 33 17 .32 .56 1.02 .69 .32 .39 1 .36 Anesthetic 2 .88 51 .42 (A) 3 1.53 49 .30 ΣΣή-13.7980
Consider the linear model y=B,+B,x,+B,x,+B,x+P+u, You estimate the model y=B,+B,x,+B,x, observations and obtain the OLS residuals . You then estimate the auxiliary regression +u based on 123 31 3 31 44i The LM statistic 3i +1 4/ you obtain to test the null hypothesis that H:B,=B,=0 is 20.91. What is the R2 of the auxiliary regression? It is not possible to say 0.17 O 0.175714 O 0.177203
Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usual random error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0 were tested and Ho: B₁ = 0 was rejected. Assume ₁e₁² = 0. ei i) Briefly explain what the conclusion of the test means for the values of Y given the values of X. -1 ii) Draw an example of a scatter plot with the fitted regression line for the problem mentioned above. iii) Calculate and interpret the correlation coefficient for the problem at hand.
M3
9) Find L3.2 (5) using the nodes xo = 3,x1 = 4, x2 = 6 ,x3 = 8 %3D
A youtuber is interested about the participation of its viewers in the games they watch him play on his channel. The youtuber wants to compare the views he gets from them watching fortnight vs the views he gets from them watching the game Among Us. Use the data given and show in an Excel work sheet to test at an α=0.01 level that there is a difference in the proportion in the number of views he gets from fortnight compared to the views from Among Us. Fortnight Among Us Total Viewers 35 23 58 Non-Viewers 69 53 122 Total 104 76 180 What is the Null and alternative hypothesis? what would be the Point estimate? P-value? Decision? Interpretation including whether there is evidence in a difference in proportion views fortnight game vs Among us game
The article "Permeability, Diffusion and Solubility of Gases" (B. Flaconnèche, et al., Oil and Gas Science and Technology, 2001:262–278) reported on a study of the effect of temperature and other factors on gas transport coefficients in semicrystalline polymers. The permeability coefficient (in 10-6 cm³ (STP) / cm · s· MPa) of CO, was measured for extruded medium-density polyethylene at both 60°C and 61°C. The results are as follows: 60°C: 54 51 61 67 57 69 60 60 63 62 61°C: 58 60 66 66 68 61 60 Find a 95% confidence interval for the difference in the permeability coefficent between 60°C and 61°C.
7B A study was conducted that measured the total brain volume (TBV) (in mm3) of patients that had schizophrenia and patients that are considered normal. Table #1 contains the TBV of the normal patients and Table #2 contains the TBV of schizophrenia patients ("SOCR data Oct2009," 2013). Table #1: Total Brain Volume (in mm3) of Normal Patients 1663407 1583940 1299470 1535137 1431890 1578698 1453510 1650348 1288971 1366346 1326402 1503005 1474790 1317156 1441045 1463498 1650207 1523045 1441636 1432033 1420416 1480171 1360810 1410213 1574808 1502702 1203344 1319737 1688990 1292641 1512571 1635918 Table #2: Total Brain Volume (in mm3) of Schizophrenia Patients 1331777 1487886 1066075 1297327 1499983 1861991 1368378 1476891 1443775 1337827 1658258 1588132 1690182 1569413 1177002 1387893 1483763 1688950 1563593 1317885 1420249 1363859 1238979…
Consider the simple regression model Yi = B1 + B2r; + €i, E; n iid N(0, o²) with pdf for observation i is given by: 1 exp 1 (yi – B1 – Bori)²] V2no? o2 a. Given the iid sample (y1, r1),..., (YN, rN), derive the maximum likelihood estimator of Bo and B1. b. Derive the variance of the maximum likelihood estimator of Bo and B1. c. Show that maximizing the log L(B,02|y, r) corresponds to minimizing SSR.
Suppose we take a random sample of size 25 form Bi(10, p). Find the pmf and the CDF of the 5th order statistic Y3.

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