Q. Suppose that independent random sample of size 11 and 2 are to be selected from normal populations with means 11 and 112 , respectively, and common variance \sigma ^{2} . For testing ?? : 11 12 versus HO : H1 - H2> 0(o unknown , show that the likelihood ratio test reduces to the two-sample t test presented in Section 10.8.

It is from Mathematical Statistics with Application(7th edition) Exercise 10.112, and I couldn't understand the whole process of solution. Could you please explain more detailed solution to this problem?

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A nonconducting infinite plane sheet of charge has a uniform positive charge per unit area o. To find the electric field E using Gauss's Law, you draw a cylindrical Gaussian surface of length L and cross- the picture. sectional area A that goes through the charged sheet, as shown in E Gaussian X surface X x x X X X X X X X X X X X X X X X X X X VX X XXIX X X + + +++ X Gaussian surface E What is the total electric flux through the Gaussian surface? O = EAL O D = 2EA O Q = EA O D = 2REAL8) A negative charge, if free, tries to move A) in the direction of the electric field. B) from low potential to high potential. C) from high potential to low potential. D) away from infinity. E) toward infinity. 9) Gaussian surfaces A and B enclose the same positive charge +Q. The area of Gaussian surface A is three times larger than that of Gaussian surface B. The flux of electric field through Gaussian surface A is A) nine times larger than the flux of electric field through Gaussian surface B. B) unrelated to the flux of electric field through Gaussian surface B. C) equal to the flux of electric field through Gaussian surface B. D) three times smaller than the flux of electric field through Gaussian surface B. 10) If the electric field is in the positive x direction and has a magnitude given by E = Cx, where C is a constant, then the electric potential is given by V= A) 2Cx B) -2Cx C) Cx3/3 D) -CP3/3 E) -3Cx 2Individuals who want to work, but have given up searching for ajob because of limited prospects, are known as o discouraged workers. 0 frictionally unemployed. O marginally attached workers. This group. consisting of individuals who would like to work but have not looked for work during the past four weeks, is included among 0 the structurally unemployed. O discouraged workers. 0 minimally attractive workers. 0 marginally attached workers. Individuals who are involuntarily working parttime are considered 0 structurally unemployed. O frictionally unemployed. O marginally employed. 0 underemployed. By excluding the groups identied in the previous questions, the U.S. Bureau of Labor Statistics calculation methods 0 overstate the true level of unemployment. O accurately reect the true level of unemployment. O understate the true level of unemployment