Identifying the Parameter to be Tested Lesson 2 Given a Real-Life Problem What's In Typically, in a hypothesis test, the claim being made is about a population parameter (one number that characterizes the entire population). Because parameters tend to be unknown quantities, everyone wants to make claims about what their values may be. For example, the claim that 25% (or 0.25) of all women in our community have varicose veins is a claim about the proportion (that is the parameter) of all the women in the community (that's the population) who have varicose veins (that's the variable - having or not having varicose veins). What we are typically after in a study is the parameter. What's New Consider the following examples below Example # 1: Suppose we study the population of dogs in Mandaue City. Answer. A parameter of this population would be the mean height of all dogs in the city. Example # 2: We will consider a study of high school seniors in Carcar City. Answer. A parameter of this population is the standard deviation of grade point averages of all high school seniors. Example # 3: Identify the parameter in the given situation: NegOr_Q4_Stat_and_Prob11_Module1_v2 We consider all of the likely voters for an upcoming election. There will be a ballot initiative to change the state constitution. We wish to determine the level of support for this ballot initiative. Answer: A parameter in this case is the proportion of the population of likely voters that supports the ballot initiative. What is It A parameter is a numerical value that states something about the entire population being studied. For example, we may want to know the mean wingspan of the American bald eagle. This is parameter because it is describing all of the population. Parameters are difficult if not impossible to obtain exactly. On the other hand, each parameter has a corresponding statistic that can be measured exactly. There is a simple and straightforward way to remember what a parameter is measuring. All that we must do is look at the first letter of each word. A parameter measures something in a population. Important problem of statistical inference is the estimation of population parameters or briefly parameters (such as population mean, variance, etc.) from the corresponding sample statistics or briefly statistics (i.e. sample mean, variance, etc.) A BC What's More Identify the parameters to be tested in the given situations. 1. A university claims that working students earn an average of 20 pesos per hour. 2. The manufacturer of new GVX Hybrid car claims that it gets an average of 52 miles per gallon of gas.What I Can Do Activity 5 Do what is asked. Consider the situation below. The body mass index is calculated by dividing a person's weight by the square of his/her height. That is, body mass index equals weight/(height) . This measure determines whether a person is overweight or not. Suppose that a person is overweight if his/her body mass index is above 24kg/m and a random sample of 20 individuals from a certain place have the following body mass indices: 24.2 33.1 24. 29.9 30.4 32.8 17.5 23.1 28. 24.2 27.8 29.4 19.6 28.5 28 25.7 22.0 29.0 35.9 18.5 Would you say that the people in that place are overweight? Test at 5% level of significance. Given a real-life situation above, find the following: (1 point each and additional 1 point for every solution) 1. *= 2. S= 3. Ho= 4. Ha = 5. U= 6. 0= 7. Ze or to = 8. Za or ta = 9. Decision rule: 10. Draw the rejection region 11. Decision: 12. Conclusion: NegOr_Q4_Stat_and_Prob11_Module3_v2 12