Frequently Asked Questions (FAQ)

• How do the quizzes help prepare us for the tests?
• What should I do if I need to miss a class?
• What is the meaning of linear transformations?
• How do you "eyeball" the mean, median, and midrange from density curves?
• What do al the symbols used in the course mean?
• What is a real world use for confidence intervals?
• Should I drop this course?
• Why do you call on people in class?
• Where can I get additional help for this course?
• Why are the formulae used in class different from the formulas in the texts?
• When I use the definition, I come up with different values for the quartiles, Why?

• How do the quizzes help prepare us for the tests?

  This quaestion was from when I gave T/F quizzes, which quizzes were generally more conceptual (abstract), while the tests are more computational (concrete). Indeed the concepts helped you understand some of the computations, but the quizzes tested a different aspect of the course than the tests.

  The present takehome quizzes are very similar to problems you will see on the tests.

  The written correspondence assignments tend to be more conceptual than computational.

• What should I do if I need to miss a class?

  The most important thing is to not fall behind. The recommended readings and problems, although not dated, are in order on this webspace. The "lecture summaries" on this webspace present my focus on the material. You should check with someone in the class to see what I did in class (their perception of what was of interest is probably closer to your perception than my opinion). You can also contact me if you have any questions. It is a courtesy to send me an e-mail if you know in advance that you will miss a class. I do not give make-up quizzes, but make-up tests will be administered if a test is missed.

• What is the meaning of linear transformations?

  When dealing with real data, it is usually recorded with units such as inches, dollars, or degrees Fahrenheit. Someone may may be more familiar with units such as centimeters, pounds sterling, or degrees Celcius. Changing measurements from one set of units to another is achieved with (usualy) linear transformations such as y=2.54x (inches to centimetres), y=.57x (dollars to pounds), or y=.56x-17,78 (Fahrenheit to Celcius). Multiplication in such transformations (e.g., by 2.54, .57, or .56) results in the measures of location (mean, median, etc.) and measures of spread (standard deviation, inter-quartile range, etc.) being multiplied by the same factor (the variance is multiplied by the factor squared). Addition (e.g., subtracting 17.78) shifts the measures of location by adding that quantity to them, but leaves the measures of spread unchanged. In a sense none of the measures of spread or locaton are changed when units are changed, since a mean temperature of 41F is equal to a mean temperature of 5C and a standrd deviation of 4F is equal to a standard deviation of 2.22C.

• How do you "eyeball" the mean, median, and midrange from density curves?

  The midrange is the half way between the maximum and minimum, if the data distribution is not bounded (e.g., the normal distribution which can take all values from negative infinity to infinity), there is no midrange. The median is the middle in the sense of an equal number of data points on each side, which means equal area under the curve for continuous distributions. The mean reflects the distance of the points, not just the number of points, hence a long tail (a few distant points) on one side (the distribution is said to be skewed in that direction) will cause the mean to be that side of the median.

• What do all the symbols used in the course mean?

  I do not know where there is a compilation; specific symbols may be listed in the index to the text. Other texts have lists of formulae, which may contain some of the information you want.

  x-bar (an overscored x) is the mean of a sample (the average weight of 20 students) mu (the lower case Grek letter) is the same as E[X], the mean of the population or the theoretical mean for a probability distribution function.

  sigma (lower case Greek letter) is the standard deviation of the population or the theoretical value for a probability distribution function; s is an eastimate for sigma based on a sample (s^2 is the the unbiased estimator for sigma^2 from a sample of a population). (We divide by n-1 to get s because we do not know the true mean of the population and there is other sampling error.)

  p-hat (p with a caret (^) circumflex above it) is the proportion in a sample (the percentage of 248 Iowans interviewed who approve of Clinton)
  p is the actual proportion in the population (All Iowans, all voters)

  sigma sub x-bar is the standard deviation among all possible values for x-bar (for the given sample size); sigma sub x-bar is sigma/SQRT(n)
  sigma sub p-hat is the standard deviation among all possible values for p-hat (for the given sample size; sigma sub p-hat is SQRT(p(1-p)/n)

  z sub alpha (z with a subscript of the Greek letter alpha) is the z-score beyond which alpha remains in the tail. Hence z_.02 is 2.05
  N.B.: You will often see z_(alpha/2), in which case (alpha/2) is the area in the tail beyond the specified z value; alpha is the area in both tails that far away.

  (1-alpha) denotes the level of confidence in a confidence interval
  alpha denotes the level of significance in a test of significance.
  P (upper case) denotes the level of significance of an observation; this is essentially the same as alpha above.

• What is a real world use for confidence intervals?

  When the Des Moines Register reports that 73% of the people approve of Clintons policy in Lesser Antilles, with a margin of error of 2.5%, they are saying that the [95%?] confidence interval for the percent of people who approve of Clinton's policy is (.705, .755).

• Should I drop this course?

  Many students do not do as well on early tests as they had anticipated. This in part reflects that since only the top half of the high school students come to UNI, people who were in the middle of their high school class are at the bottom of UNI. Mathematics for Decisionmaking is intended to be a less difficult general education course. If you are required to take Introduction to Statistical Methods for your major (e.g., business), Analysis for Business will strengthen your mathematical skills before you take this class. (My personal opinion is that, for students without precalculus, Analysis for Business is more important for Introducton to Decision Techniques ("Quantitative Methods", finite math) than for Intro Stat Meth.) "Equivalent" courses at some community colleges may be less difficult (many students like to take summer courses at their local community college), but if you do not have a foundation of the material, subsequent courses such as business statistics will be more difficult. If you need to take this course twice to master the material, dropping it after 3 weeks each semester will never give you enough time devoted to this course. But if you are having difficulty in most of your courses, you should drop one so you can focus your attention on the others. My general advice is, if you need this course for your major, do not drop it, unless you are also having difficulties in other courses.

• Why do you call on people in class?

  There are several reasons. One reason is that it slows down the pace of the lecture thereby allowing students a little time to comprehend the material. Another is that it gives me a little feedback as to what is understood by the class. A third is that by asking the students to speak in class, they will gradually become more comfortable with speaking in large groups, in other contexts as well as in class. A fourth is that it is good practice for when one does not know the answer, to provide whatever useful informaton he/she can.

• Where can I get additional help for this course?

  I hope my webspace provides significant support. If you want someone to talk with, there are students and a professionsl who will provide free assistance with the material in this course in ITTC 008 (the former East Gym). If you want to hire a tutor, the Mathematics Department office maintains a list of students you can hire. Of course, you can also visit me in office hours (catch me after class to schedule a time).

• Why are the formulae used in class different from the formulas in the texts?

  They are not really different, merely rearranged. This refers to the variance, standard deviation, correlation, and similar statistics. [SUM](x(i)-(x-bar))^2 = ([SUM](x(i))^2)-n(x-bar)^2; the right hand side is more efficient computationally, but I prefer the left hand side, since you can intuitively see what you are measuring. A similar rearrangement occurs with the calculation of the correlation. The formulae I use as well as the computationally efficient formulae are both in the present text.

• When I use the definition, I come up with different values for the quartiles, Why?

  Although the intuitive concept of dividing a data set into fourths is clear, the actual implementation is not. There are several differnt interpretations of the definition, which will sometimes provide different values. Minitab (on the mainframe) uses different definitions of quartiles in Describe and for its Boxplot. The text uses percentiles to define quartiles (but the text's definition of percentiles is only one of many that are in use). I may use various definitions, not necessarily the one I prefer; you are welcome to use any (reasonable) definition.

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