Winter, 2012 Thursday, Jan. 19Stat 217 – Day 10Sampling from Finite Population(a) Select a representative set of 10 words from the passage by circling them with your pen or pencil.The above passage is, of course, Lincoln’s Gettysburg Address, given November 19, 1863 on the battlefield near Gettysburg, PA. We are considering this passage a population of words, and the 10 words you selected are considered a sample from this population. In most studies, we do not have access to the entire population and can only consider results for a sample from that population, but to learn more about the process of sampling and its implications we will next deal with a hypothetical scenario where we sample from a known population.1Four score and seven years ago, our fathers brought forth upon this continenta new nation: conceived in liberty, and dedicated to the proposition that allmen are created equal. Now we are engaged in a great civil war, testing whether that nation, or anynation so conceived and so dedicated, can long endure. We are met on agreat battlefield of that war. We have come to dedicate a portion of that field as a final resting place forthose who here gave their lives that that nation might live. It is altogetherfitting and proper that we should do this. But, in a larger sense, we cannot dedicate, we cannot consecrate, we cannothallow this ground. The brave men, living and dead, who struggled here haveconsecrated it, far above our poor power to add or detract. The world will littlenote, nor long remember, what we say here, but it can never forget what theydid here. It is for us the living, rather, to be dedicated here to the unfinished workwhich they who fought here have thus far so nobly advanced. It is rather forus to be here dedicated to the great task remaining before us, that from thesehonored dead we take increased devotion to that cause for which they gavethe last full measure of devotion, that we here highly resolve that these deadshall not have died in vain, that this nation, under God, shall have a new birthof freedom, and that government of the people, by the people, for the people,shall not perish from the earth.Winter, 2012 Thursday, Jan. 19(b) Record each word from your sample, and then indicate the length of the word, whether or not the word is a noun.Word Length(no. of letters)Noun?(Y or N)1.2.3.4.5.6.7.8.9.10.(c) Identify the observational units and the variables you have recorded on those observational units. (Keep in mind that observational units do not have to be people!)(d) Classify each variable as quantitative or categorical.(e) If you wouldn’t to examine a graphical display of your results, what type of graph would you construct forLength of letters? Whether or not noun? When we are sampling from a finite population (e.g., all 268 words), we can consider the parameter to be a numerical summary of the variable in the population. With quantitative variables, we will often be interested in the population mean. With categorical variables, we will often be interested in the population proportion. To distinguish these values from the corresponding statistics, we will use Greek letters, for a population mean and for a population proportion. If these values were instead computed about sample data, they would bestatistics (e.g., , pˆ).(f) Calculate the average length of the 10 words in your sample. Is this a parameter or a statistic? Explain how you know. What symbol could you use to refer to this value?(g) Calculate the proportion of words in your sample that are nouns. Is this number a parameter or a statistic? Explain how you know. What symbol could you use to refer to this value?2Winter, 2012 Thursday, Jan. 19(h) Did everyone in class obtain the same values for their sample mean or their sample proportion?(i) Pool together your results to look at dotplots of the sample mean lengths for each student.Label:(j) The average length of the 268 words in entire speech equals 4.29. Is this number a parameter or a statistic? Explain how you know. What symbol could you use to refer to this value?(k) The proportion of all words in the entire speech that are nouns is .16. Is this number a parameter ora statistic? Explain how you know. What symbol could you use to refer to this value?(l) Do you think the words you selected are representative of the 268 words in this passage? Suggest amethod for deciding whether you have a representative sample. [Hint: Whereas any one sample may not be produce statistics that exactly equal the population parameters, what would we like to be true in general?](m) How many students in your class obtained a sample average number of letters that was larger than4.29? How many students in your class obtained a sample proportion of nouns that is larger than .16? Definition: A sampling method is biased if the results from different samples consistently over or underestimate the population parameter of interest.(n) What do the answers to these questions in (m) tell you about whether the sampling method of asking you to pick 10 representative words is biased or unbiased? If biased, what is the direction of the bias (tendency to overestimate or to underestimate)?(o) Explain why we might have predicted in advance that this sampling method (asking you to pick 10 representative words) was likely to be biased.3Winter, 2012 Thursday, Jan. 19(q) Suggest another technique for selecting 10 words from this population so that you do think the measurements of length and noun/not noun are more likely to be representative of the population?Taking a simple random sample(r) Instead of having you choose “random” words, take a simple random sample of words and evaluate your results. The first step is to obtain a sampling frame where each member of the population can be assigned a number. On the Lecture Notes webpage, you will find a link to the entire passage which a number in front of every word. For example, the 43rd word is nation. Go to the website http://www.random.org. On the right hand side of the page, you can enter a min and max, enter 1 and 268, respectively. When you click “Generate” you will have generated a single random number between1 and 268. Do this ten times (extra times if you get repeats). Enter the random numbers in the table below:Randomly generated ten ID values from 1-268(s) Using your randomly generated values, look up the corresponding word from the table on this and the next page. Fill in the data table