Answer the 2 questions under ELABORATE: ACTIVITY ALERT! Laboratory Activity 2

ELABORATE: Activity Alert! n Laboratory Activity 01: Consuucting a Normal Distrlhutlon Let us try to estimate the mean of the population by combining three samples independently. and then get their average. The possible combinations are already shown for your convenience. is reminded that sortie parts of this activity are ungradad. but you mars to three creations attheendoftheactivttyetegraded. Let us assume the figure below [the square) as our population. and we are going to estimate the mean attribute or parameter oi the population. The same population is divided into four samples which bear the parameter. 1 2 3 4 Assume further that the attributes are not equal since members of the population have various levels of this attribute. Let us say that the attributes In Samples 1. 2. 3 and 4 have measurements of 1. 2. 3. and 4 too. respectively. If we get the mean attribute of the popuiatlon based on each sample attribute. that would be: Mean={1 +2+3+4ir4=1i Oops. pause for a minute! Please read the preliminary explanations first before doing the actual activity. Trust me. you need the clericatery statements below. Be. the mean attribute of the population Is 2.5. This Is the expected mean value of the attribute of the population. But I would like you to remember that the attributes of a population vary greatly. Let us take for example. mean score in a science literacy test. If the mean score of students in this test Is 35 out of 50. there is a high chance that the individual scores may be higher or lower than the mean. This can be related to various factors such as prior knowledge about science concepts. reading comprehension. to. motivation. analytical skills ~ and so on! The same is true for health. Health Is inuenced by various metabolic. environmental. behavioral. social. demographic factors that it is difcult to compare samples merely by comparing the mean. But if you include everybody In the population to develop an inference. it will take you decades of research before a suggestion is accepted to develop a health policy. By that time. your results are already Invalid. Hence. it Is important to understand a population distribution and how it can be used to infer an attribute of a population. This wear. the inference becomes valid In a probabilistic context. Next, tally your results. Refer to your output in the previous page. What are the different values of the mean attributes that you have obtained? After writing them below, count the number of times that each mean attribute appears. Mean Attribute Number of Times it Appears Lastly, plot the mean attribute in the x-axis of a graph and the frequency of each mean attribute in the y-axis. The graph is already provided for your convenience. 14 12 10 Frequency 2 0.5 1.5 2 2.5 3 3.5 4.5 Computed Mean This part of the activity is ungraded. Do not proceed to the next page if you did not answer these activities yet, OK?OK, pause and digest that information first. The next part of this activity is graded. Please follow the instructions before submitting your output online. Since the activity is based on realizations, you don't have to provide references to your answers. Use appropriate terms and briefly explain using concise statements. ELABORATE: Activity Alert! 090-00 Laboratory Activity 02 Testing Your Understanding of Population Distribution Graded activity worth 20 points. Based on your realizations, answer the following questions using a maximum of FIVE sentences only. Your answers to these questions are GRADED. Submit your answers in a pdf of Word format to the submission bin for Laboratory Activity 02. 1. Based on the activity you performed, why is random sampling required when inferring from the population distribution curve? Discuss two reasons concisely. (10 points) 2 What will happen to the distribution if more samples and more attributes are included? Why do you say so? (10 points) Additional Instructions: Download the template in your module site, under "Module 4 Answer Sheet Template." Write your name and Class Code in ALL pages of your output. Font type and size: Arial, 11 Name your output using the formatbelow: Class Code_Lab Activity 02_Surname, First Name, Middle Initial Answers will be evaluated using a rubric. Good luck! Activate your neurons!If you plot the frequency on the y-airls and the mean attributes In the xairis. your graph should look like this. 14 12 I I to C I U a E E. ii I I I. 4 I i 2 I I I! ii 0.5 1 1.5 2 2.5 1 3.5 4 1.5 Computed Heart i' hope you got the same answer! Again. you can ask your facilitators for clarifications. Now. read the post-laboratory explanations below. Based on random sampling that we did. the frequency of getting 2.5 as the average is larger titan the frequency of getting a smaller or bigger value. In this case. we have plotted the probability of getting the attribute of the population based on our randomly picked samples. 111i: plot of values is the sample distribution curve. Sampling distributions serve twopurposes: (1) they allow us to answer probability questions about sample statistics. and [2] they provide the necessary dreary for making statistical inference procedures valid. Notice that it resembles the norms! distribution curve. Now, the curve becomes more similar to the population curve if the range of attributes and samples are increased. Of course. when sampling Is not ideal or lacks representatlvanass of the population. there will be errors. imagine an epidemiologist making an error In controlling communicable diseases! Lin acceptable. right? To guide a researcher in sampling. the central limit theorem is often used. Carmel Limit "theorem: Given any population with mean m and variance s2. the sampling distribution of x will be approvinutely normal with mean m and variance sz-n when the sample size n is large. EVALUATE: Did you get it right? 00000 Answers to Laboratory Activity 01 Let us see if you have arrived at the following results: Combination of Estimated Mean Combination of Estimated Attributes Attribute Attributes Mean Attribute 1 3 1 1.67 1.33 3 2 2 1.67 1 2.33 4 2 3 1 4 2.67 2 1 1.33 3 2 2 2 2 1.67 3 2 2 2.33 2 3 2 3 3 2.67 2.33 3 W N W W N N 1.67 2.33 2 3 2.67 3 2.33 3 AA W W W 4 2.67 3.33 2 3 2.67 2 2.33 3 3 4 3 2.67 3.33 4 4 3 3.67 N 1.33 1 2 AAAAWW 1.67 2.33 N N A W N - 2 2.67 2 2.33 A W N - A W N - A W N - A W N - A W N - A W N - A 3 1.67 4 2.33 N N N N 2 2 4 2.67 N 3 2.33 4 3 2.67 3.33 2 AA AA W WW W N N N N- - - AAA 2.67 2.33 3 2.67 4 3.33 3 W N - A W N - 3 3.67 NNNNNN NN 2.33 3 2.67 AAAAA 3.33 AAAA 3 3.67 3.33 4Let us say. we picked three random samples and estimated the mean attribute of the population as discussed In the previous page. l have enumerated all probable combinations below. You may useI a calculator or MS Excel for the computation. Manual computations are radians. right? But leaminp a concept does take patience and dedication. So. don't fret on math operation s