From this two photo it shows 3 different forms of formula for my biostatistic subject. I want to ask in this 3 different formula how can I differentitate on which formula to use on what type of question. Tests on Means for Two sample casesFor two independent samples, the following table presents the structure of the null hypothesis,the test statistics to be used, the different forms of alternative hypotheses and theircorresponding critical region.Case 1: 0₁² and ₂² are knownHoH1 - H2 = doTest statisticZ=(x₁-x₂)-do01²n102²n2+HaH1-H2 < doH1 - H2> doH1 - H2 # doCritical region(the average weights of girls and boys do not differ)Z<-ZaZ> ZaIZI> Za/2Example: A weight loss management program was given to obese children; 50 girls and 75 boys.After the program, the girls made an average weight of 80 kilos with a standard deviation of 4 andthe boys had an average of 86 kilos with a standard deviation of 6. Is there sufficient evidence at0.05 level of significance that the average weight of girls and boys differ?Solution: Let μ₁ = average weight of girls and μ₂= average weight of boysStep 1. Set the null and alternative hypothesesHo H₁ H₂OR (can be written this way)H₁ H₁ - H₂ = 0 (there is no significant difference between the average weights of girls and boys)Ha μ₁ μ2 (the average weights of girls and boys differ)OR (can be written this way)Ha : μ1 - U2 #0 (there is a significant difference between the average weights of girls and boys)Step 2. The level of significance is set at a = 0.05This means that we are willing to commit a 5% chance of committing a Type I error; that is,rejecting the null hypothesis when it is true.Since, the alternative hypothesis is non-directional, used the two-tailed test, thus divide alpha valueby 2, %/2 = 0.05/2 = 0.025. and boys.● Case 2: 0₁² = 0₂² but unknownH₂Name:Section:μ₁-μ₂= dosp=H₁-H₂= do(x₁-x₂)-do1 1sp n₁ 1₂df=v=n₁ + n₂-2Schedule:dfTest statistict =Case 3: 0₁²0₂² and unknownH₂(n₁−1)s₁²+(n₂−1)S₂²n₁+n₂-2t =Test statistic(x₁-x₂)-do721 722n1n₁-1++$₂²n₂n₂-1H₂H1-H₂ doμ1-μ₂ #doH₂H₁-H₂ < doH1-H₂> doH₁-H₂ # doCritical regiont<-tat> ta|t|> ta/2Class number:Date:Critical regiont<-tat> to|t|>ta/2Example: A group of researchers selected 50 countries and classified them according to three GNP levels:Low (less than $50B), Moderate ($50B - $174B) and High (above $175B). For each classification, the averagelife expectancy was determined:

Given information: Three different formulas for t-test are given.

For two independent samples, the following table presents the structure of the null hypothesis, the test statistics to be used, the different forms of alternative hypotheses and their corresponding critical region.

For two independent samples, the following table presents the structure of the null hypothesis, the test statistics to be used, the different forms of alternative hypotheses and their corresponding critical region.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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