Stat303: Statistical MethodsHomework 3 (07/14/2009)Instructor: Anh DaoProblem 1 Look at the Bias and Variability chart at the end of section 3.3. Then look for the histogramwhich match with the give conditions for bias and variability.Problem 2(a) Identify the type of design used in the study.(b) Identify the method of sampling used.(c) Identify the type of design used in the study.Problem 3Look at the Bias and Variability chart at the end of section 3.3 to identify situation of high bias (meanscenter of the statistic’s distribution is far from the population mean) and low variance (when data isclustered as a close group).Problem 4(a) Recall, the explanatory variables form the factors in a study so try to identify the explanatoryvariables (those variables whose effect on the response is of interest in the study).(b) The treatments are combinations of levels of factor. Example: If there are two factors one with 2levels and other with 4 types then the number of treatments is 2 × 4 = 8.(c) In replication the treatments needs to be applied to many units.(d) There are two groups: paperback and hardback then from each of the two groups randomlydifferent types of glues are assigned, now identify the type of sampling method.Problem 5 In random number table if we sample more than once then the second sample may/may notbe same since in random sample anything can happen.Problem 8“Which of the basic principles of statistical design were used in this study?”Choose for your answer: control, randomization, repetition, blinding.Now, create a list of random numbers given the sequence in your homework problem. Suppose, if thesequence of random number look like: 73924 28444 10384 83920 02055 67433 84374 92373 55232 1188685325So you can chop this sequence off into 2-digits numbers: 73, 92, 42, 84, 44, .... ,Use the idea that only units 01 through 49 can be present since there are no observations beyond 49so if you choose a number like 73 then it is incorrect since it is greater than 49.Fill in the numbers from 01 to 49 beginning with the first row and go from left to right. The firsteligible number would be 42.12 Homework 3Problem 10 This is still a random sample so the statistic, the sample proportion is unbiased which meanscenter of the sampling distribution is the true population proportion, the parameter being estimated.The only difference is in sample size, which increases from 60 to 200. As the sample size increases thespread of the sampling distribution decreases.Problem 11 Keep two things in mind:1. The larger the sample the smaller the variability.2. Sampling should be done from entire population that we are interested in not just a part of it.Problem 12 b. Sampling variability depends on sample size not population size. If the sample size doesnot change than the variability would not
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