Stat 2000 Tips for Assignment 3
Published: Tue, 10/19/10
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Throughout the term I will send you all sorts of tips to help you study and learn the course. You probably already have done so, but, if not, I strongly recommend you purchase my Basic Stats 2 Study Book. You will find it a great resource to learn the course. I pride myself in explaining things in clear, everyday language. I also provided numerous examples of all the key concepts with step-by-step solutions. You can order my book at UMSU Digital Copy Centre at University Centre at UM campus. They make the book to order so please allow one business day. The book is split into two volumes and each volume costs $45 + tax.
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Tips for Assignment 3: Anova and Probability Distributions
Study Lessons 5 and 6 in my book, if you have it, to prepare for this assignment. Those of you with an older edition of my book will have to study Lessons 5, 6 and 7.
For Question 1, note that ni simply means they want you to tell them the values of n1, n2, etc..
For Question 2, you should certainly use the stat mode in your calculator to compute the means and standard deviations (which will, of course, enable you to know the variances), then do the rest of the problem by hand using the formulas for SSG, SSE, MSG, MSE, and F. Make sure you have memorized those formulas (and the formula for the overall mean or grand mean). There is almost certainly going to be a question or two on the exam that will check to see if you know these formulas (although it is rare to see an exam question that makes you do an entire ANOVA by hand). It is common that an exam will make you compute MSG or MSE by hand having been given the sample means and standard deviations.
Here is how to do the JMP part of Question 3:
It is done the same way you did the JMP in Assignment 2. Open a New Data Table and type the data in manually in this manner (don't bother pasting and stacking, it is not worth the effort): Name your first column "Silver" or something like that, and type all the silver contents down that column. Which is to say, type in the numbers from the First coinage down the column, then continue to type all the numbers from the Second coinage, and finally continue to type all the numbers for the Third coinage. Double click at the top to the right of the "Silver" column heading to create a new column and name it something like "Coinage". Down that column type "First" repeatedly down that column in all the rows that have the data for the First coinage. Then type "Second" repeatedly down the column in the rows that have data for the Second coinage. Finally, type "Third" for the rest of the column. You may want to type the phrase once and then copy and paste it down the rest of the relevant rows to ensure there are no typos. Once you have done that, double-click the "Coinage" column heading and confirm that the Data Type is Character and the Modeling Type is Nominal and click OK.
Select Analyze, then Fit Y By X. Highlight the numeric column "Silver" and click the Y, Response button. Highlight the character column "Coinage" and click the X, Factor button. Click OK.
You should now see a graph with three vertical arrays of dots showing the silver content for the three different coinages separately. Click the red triangle and select "Means and Std Dev" to get a summary of the means and standard deviations of the three samples. Click the red triangle again and select "Means/Anova/Pooled t" to get the output you need.
By the way, be sure to study my questions 5 and 6 in Lesson 5 thoroughly to better understand what they are getting at in part (d).
In Question 4 the applet is pretty straightforward to learn from. Note that the pooled standard error is essentially MSE. Remember, F = MSG/MSE and think about what affects the value of MSG and MSE and how those two values affect the value of F. The applet pretty well teaches you what happens. Messing with one part changes MSG, messing with the other part changes MSE.
Do the JMP in Question 5 just like I showed you what to do in Question 3 above. Here at least you can copy and paste the data into JMP. Be sure to paste it into JMP by selecting Edit, then, while holding down the Shift key, select Paste in order to paste the column headings properly (or, after you have copied the data, select "Edit" then "Paste with Column Names"). Note, double-click the "bfed" column and confirm that its Data Type is Character and Modeling Type is Nominal; double-click the "energy" column and confirm that its Data Type is Numeric and Modeling Type is Continuous. Always make the numeric column Y and the character column X when you select Fit Y By X.
Re-read my section on the P-value in Lesson 2 of my book if you still are not sure how to interpret a P-value.
For Question 6, use the formulas for mean and standard deviation I teach in Lesson 6 and use in my questions 1, 2 and 3 (questions 1 and 2 if you are using an older edition). By the way, someone has pointed out that my answer to question 2 in my new edition (blue book) is wrong. The mean daily income is $188, not $192. I forgot how to add that day.
For Question 7, if you believe the scenario is Binomial, the parameters you need to list are n and p. If you believe it is Poisson, the parameter is λ. If you don't have the required parameters, then it could not be that distribution.
For a binomial distribution, there must be a fixed value of n, a fixed value of p, the trials must be independent, and each trial must have only two possible outcomes (Yes/No; Success/Failure; Liberal/Not Liberal, etc.) and X can have values 0, 1, 2, . . . n.
For a Poisson distribution, there must be an average number of "things" and X = the number of "things" and can have values of 0, 1, 2, 3, . . . infinity.
For Question 8, read my tricks on how to work with Table C (in Lesson 6, or Lesson 7 if you have an older edition) in case your value of p is not actually on the table, but its complement is (question 7 in Lesson 6 of my book is a good example; that is question 4 in Lesson 7 if you have an older edition). In part e, simply compute μ +/- σ to find the desired range (you, of course, computed μ and σ earlier in the question) and then find the probability that X is a value within that range, the usual way for binomial problems, remembering X is discrete. This question is demonstrating that a binomial distribution is not a normal distribution. You may recall from Stats 1, the 68-95-99.7 rule. If this were a normal distribution, 68% of the X values would be within one standard deviation of the mean. In a binomial distribution, we have no idea what the percentage will be. It depends on n and p. Some of you may get values near 68% and others will get totally different percentages.
For example, if you find that the mean is 11.2 and the standard deviation is 3.1, then X can be anywhere between 11.2 - 3.1 and 11.2 + 3.1. Which is to say, X is anywhere between 8.1 and 14.3. Since X is discrete, that means X can be 9, 10, 11, 12, 13, and 14. Add those probabilities up.
For Question 9, part e you can use the techniques I show starting on page 339 of my book and illustrate in questions 11 and 12 of Lesson 6.
Those of you who have an older edition of my book can use the techniques I show in questions 8 and 9 in my Lesson 7, but do not do the continuity correction! Which is to say, do not add or subtract an extra .5 to the x-values. For example, in my question 8, part (b), you would find the area between 30 and 50 (the given range of x values), not the area between 29.5 and 50.5. They are not teaching the continuity correction any more (I think).
In that respect, do not even bother doing any of the homework from the BIN section of the Cheng book since that entire section does use the continuity correction which you are not taught any more.
For Questions 10 and 11, you are dealing with standard Poisson stuff as I teach in Lesson 6 (Lesson 7 of older editions).
In Question 12, to compute a P-value in a binomial distribution, be sure to compute the probability of the appropriate tail as usual. Which is to say, in a lower tailed-test, you would want the probability that X is the given value or lower; in an upper-tailed test, you would want the probability that X is the given value or higher; in a two-tailed test, you would want to find the probability of the appropriate tail and double it to get the P-value.