would you help me with this lab, please?
Once again, we know after our discussions on sampling that each random sample gathered from a population may have different characteristics. Thus, when we calculate a statistic from those samples, there will most likely be some differences between the values. Since those values will differ, the question that becomes obvious is how we then go about making intelligent statements about the population parameter. What we will be doing in this lab is gathering several samples and noticing their different statistical values. What we hope is that while there will be differences for the samples, a noticeable pattern wl emerge. Directions: Each group will be provided with a coin to toss. i) Toss the coin 10 times and record the number of heads obtained. Based on this result, calculate the sample proportion, f)\Name: The important idea here is the following, while we can not predict what the next value of p will be if we gather a sample, we do know how repeated samples will behave over time. We also see that in this particular situation that shape is something very familiar to us. Directions: Once again you will be tossing coins to gather samples. i) Toss the coin 20 times and record the number of heads obtained. Based on this result, calculate the sample proportion, ii, of the number of heads obtained ( = # heath/90). ii) Have each member of your group gather 5 such samples and statistics. (Thus you should have a total of I 0 values for p. ) Record these values in the table below: Group Results Class Totals p Frequency iii) There will be a similar table on the Elmo for the entire class to gather their results. When you nish your group results, add them to those on the Elmo and when all the groups are nished copy the class totals to the table located above on the right. page 3 of 4 by P.30umn Name: 4. Based on the frequencies for the "Class Totals" we could sketch a histogram for these results. However, given the values obtained, we can visualize this without actually sketching the distribution. How would you describe the shape of this distribution? How would this histogram compare with the one we would get from the earlier data? Explain. 5. What do you suppose might happen if we increased our samples to 40 coin tosses? Explain why you think this is true. 6. Based on the work performed in this experiment, complete the following statements: a) It appears that sample proportion, , is an (biased/unbiased) statistic for the population proportion. b) It appears that as the size of the sample increases, the variability of the sampling distribution (increasesldecreases). c) The shape of the sampling distribution appears to be (describe shape) and that shape becomes more apparent as the size of the samples (increase/decrease). d) Since j} appears to be an (biasedlunbiased) statistic and its sampling distribution appears to be (shape), in order to understand ALL of the behavior of p values we need to only know the and of its distribution. page 4 0f4 by Bijoux: Name: Lab: Intro to Sampling Distributions The Sample Proportion Having looked at the techniques used to summarize a set of data, we begin our examination of the \"other side\" of statistics called Inferential Statistics. The idea here is to use sample data to make predictions about some characteristic of the entire population. There are several problems that we immediately encounter. As we have seen when discussing sampling, every simple random sample drawn from a population will likely be different and thus lead to different statistics. The obvious question then is how can we be sure that the one sample we draw is giving us the correct value. If the sample statistic doesn't match the population parameter, how close is it? How can we even tell the answer to that question? As you can probably see, there are a great many questions that come up here and in order to answer them we need to discuss some very fundamental topics. In order to help us begin this investigation, we will study a situation which mimics the sorts of situations in which we will nd ourselves. A sample proportion is dened to be the proportion of times that a certain outcome is obtained when an experiment is performed a xed number of times. For example, we could discuss the sample proportion of females in our class. This would be the number of females in our class divided by the total number of students. This sample value would be labeled :6 and we could attempt to use it to estimate the proportion of females here at ACC. Unfortunately, as we have discussed in class, this proportion would only be a \"guess\" and were we to use another class, the value would most likely be different. Thus, to make an intelligent statement, we need to discuss the behavior of these p values and determine whether there is a pattern to their distribution. In this lab we will be investigating the behavior of coins when ipped. While at rst this may not sound like a terribly useful activity, we will see that it introduces us to some very important ideas about the behavior of sample proportions. In fact, we will see that it actually models the behavior of some very practical situations like those discussed above. The advantage of starting with this situation is that we know in advance what the population parameter should be, and thus we can do some experiments and decide whether the sample proportion (a statistic) is a valuable tool or not. 1. Suppose we were to toss a coin a total of 10 times, approximately how many heads would we obtain? Explain your answer. 2. Suppose that you actually performed this experiment and did not obtain the exact result predicted in question 1. Would this indicate to you that the coin was "xed?" Explain why or why not. page I 0f4 by P.30uton
