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Posted:
Nov 17, 1996 10:03 AM


>From apstatlowner Sun Nov 17 04:12:07 1996 >Received: from emout08.mail.aol.com (emout08.mx.aol.com [198.81.11.23]) by cln.etc.bc.ca (8.7.6/8.7.3) with SMTP id EAA28606 for <apstatl@etc.bc.ca>; Sun, 17 Nov 1996 04:12:05 0800 (PST) >From: AlCoons@aol.com >Received: by emout08.mail.aol.com (8.6.12/8.6.12) id HAA11771 for apstatl@etc.bc.ca; Sun, 17 Nov 1996 07:11:09 0500 >Date: Sun, 17 Nov 1996 07:11:09 0500 >MessageID: <961117071108_1749469605@emout08.mail.aol.com> >To: apstatl@etc.bc.ca >Subject: Test 3 > >Hey you newbees (how do you spell that?) like me...where are your tests? How >about those of you who have been teaching stats? Lets help each other out. > Everyone was great after I posted my first two tests... very constructive >suggestions and comments. > >Please feel free to borrow any or all of this (no need to give credit). Some >of this has already been borrowed other sources. Would love your suggestions >for other problems or revisions. > >Al >====================================================================== > >11/14/96 AP Statistics  Test 3  WS/Unit 3 + BPS 3.1,2 Mr. Coons > >1. The six people listed below are enrolled in a statistics course taught by >means of television. A study requires a simple random sample of 3 subjects >to be interviewed in detail about the quality of the course. > > 1. Moore 2. Casella 3. Santner 4. Goel 5. Jones 6. Klein > > > a. Define simple random sample? > > b. Use the following list of random digits: > 27102 56027 55892 33063 41842 81868 71035 09001 43367 49497 54580 >81507 > >Start at the beginning of the list. Choose a simple random sample of three >subjects. What is the sample you obtain? > > a. Moore, Casella, Jones > b. 2, 7, 1 > c. Moore, Casella, and again Casella > d. any set of 3 names, but we must exclude Casella > >2. Some students wanted to explore the nature of the relationship between a >person's heart rate (measured in beats per minute) and the frequency at which >that person stepped up and down on steps of various heights. There were three >rates of stepping and two different step heights used. A subject performed >the activity (stepping at one of the three stepping rates at one of the two >possible heights) for three minutes. Heart rate was then measured at the end >of this period. > >a. Which of the choices below describes the study? Briefly explain your >choice. > a. It takes a convenience sample > b. It is an observational study, not an experiment. > c. It is an experiment. > >b. What is/are the factor/factors in this study? Briefly explain the term >factor in explaining your choice. > >3. Which of the following pictures depicts high bias and low variability? > > [PICTURE: THE TRADIONAL 4 PICTURES OF CIRCULAR TARGETS WITH DIFFERENT >GROUPINGS OF BULLET HOLES: MY STUDENTS HAD NOT SEEN THIS PICTURE BEFORE BUT >HAD SEEN THE PARALLEL IDEA USING HISTORGRAMS] > >4. Consider a true/false test of 25 questions on which a student guesses >randomly at each question. The following histogram presents the results of a >simulation of 10,000 such true/false tests. For example, the student answered >4 correctly on 2 of the 10,000 tests, the student answered 5 correctly on 15 >of the 10,000 tests, and so on. > > [HISTOGRAM...SEE ROSSMAN'S EXAM 2 SPRING 1996 AVAILABLE ON HIS WEBSITE] > > a. On what percentage of the 10,000 simulated tests did the student get 15 >or more correct? > > b. Do you consider the result in part "a" statistically significant? > CLEARLY explain the term statistically significant in explaining your >answer. > >5. List the three Principles of Experimental Design. For each one briefly >explain if its goal is to reduce bias or variability and why that would >happen. > >6. Joe, who is paid 2423 banana per month works in a country where the mean >monthly salary is 2010 bananas with a standard deviation of 205 bananas. > Judy, who is paid 176 oranges per month, works in a different country where >the mean monthly salary is 150 oranges with a standard deviation of 11 >oranges. Assume that salary's in each country are normally distributed. Do >some calculations and then write an convincing argument about whether Joe or >Judy has a better paying job. Make your argument in terms of the proportion >of other workers in their respective countries who make less than they do. > You may use your calculator but make sure you show some supporting work. > >7. Suppose that 46% of all American college students send a card to their >mother on Mother's Day. Suppose further that you plan to select a simple >random sample of 40 American college students and determine the proportion of >them who send a card to their mother on Mother's Day. > > a. Is 46% a parameter or a statistic? Explain briefly. > > b. Determine the probability that more than 36% but less than 60% of the >students sampled send a card to their mother on Mother's Day. You must do >this showing a completely annotated diagram , using the standard normal >table, showing your work, and writing in full probability notation. > >8. Suppose a survey of 30 voters finds that 48% of the voters plan to vote >for Ms. Brown for President rather than Mr. Jones Using your calculator if >you wish to, determine how many percentage points you would have to go on >either side of 48% to be 80% confident that the interval would include the >actual proportion of all voters who plan to vote for Ms. Brown. Note that >you will have to use 48% as your best estimate for the actual population >parameter. Show enough supporting work to convince the reader that you are >going about this problem sensibly without using trialanderror. Writing >down major calculator commands is one way to help make this clear. > >9. Observation: The formula sqr(theta(1theta)/n) guarantees that as n gets >larger standard deviation approaches zero. > > A student might suggest that this does not make sense since that in one >sample there is always a good chance that the sample proportion differs from >the population proportion. Dispel the students misconceptions and >demonstrate your understanding of the Central Limit Theorem for a Sample >Proportion by providing a detailed explanation (which you could read to a >statistics class) of why the "observation" is correct. > > end  > > > Jim Swift Haraka, Computer Coordinator, School District 70 (Alberni) haraka, 4690 Roger St, Port Alberni, BC V9Y 3Z4 hyini (250)7202762(W) (250)7234266 (Fax) Baraka



