exam01_answers_hard - STA 3024 Summer A 2011 Name Exam...

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STA 3024 Summer A 2011 Exam 1 (Form Code X) Name: UFID: This is 75 minutes exam. You have to answer 20 multiple choice questions. Each question is worth 5 points that makes the whole exam worth 100 points. There is only one correct answer for each question. You need to bubble the correct answer on the scantron to get credit. Only scantron and not this exam will be graded. You have to turn in both exam and scantron. You can use a calculator but you cannot use any supplemented materials not included in this exam. On this paper , write your name and UFID . You also need to sign and date this exam below . On your scantron , bubble your name, UFID, and exam Form Code (please see upper right corner of this page for your form code.) You also need to bubble your section number which is 1053 . There are no special codes. A formula sheet and chi-squared table are provided on the last page. On my honor I have neither received or given or planning to give any aid on this exam as well as disclose its contents to the ones who is going to take it after me. Name: DATE:

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1. Data collection. Imagine we want to know the average price of ”regular” gas in Gainesville, FL. You and your friend have driven around to collect some data. You have collected information from few gas stations and your friend has collected information from few gas stations that are different from yours. Unfortunately, you have recorded only the average of your gas stations so has your friend. Neither you nor your friend remembers sample sizes, so the only things known are two sample means and nothing else. The goal is to recover the overall mean of all gas stations that were sampled by both of you. Can we just take the mean of our two sample means to get the overall mean? Please select the best possible answer. (HINT: Think about two generic means ¯ X = 1 n n i =1 X i and ¯ Y = 1 m m j =1 Y j that correspond to our samples with sizes n and m respectively. I am asking you about the behavior of 1 2 ( ¯ X + ¯ Y ) . Try too see what happens in each scenario listed below. If you are confused and you cannot see the result analytically using the specified formula you can try to consider the example with the actual arbitrary numbers you pick as an elements of two samples. That will hopefully help you to identify the result.) (A) Yes, we can always use the mean of sample means and it will always be equal to the overall mean for the combined sample. (B) No we cannot recover the overall sample mean in this way. We need to know all the observations to do this. (C) We can recover the overall mean this way only if the sample sizes are the same. (D) We can recover the overall mean this way only if the sample means are the same. We can recover the overall mean if
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exam01_answers_hard - STA 3024 Summer A 2011 Name Exam...

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