Math 203, Introduction to Statistics,
Central College, Fall 1999 Exam 2 Review Sheet.
Tom Linton, http://www.central.edu/homepages/lintont/

Exam Particulars

The exam covers chapters 3 and 4 (section 4.6 was skipped and will NOT be on the exam) of the text (The Basic Practice of Statistics, by Moore). The exam will be open book (the text plus one page, 8.5 by 11, both sides, of notes) and calculators will be allowed. Questions on the exam will be similar (at least in the mind of the professor) to the homework assignments, however, some of the exam questions will require knowledge covered in a variety of sections of the text.

Key Terms to Know and Understand

Sample versus Population, Parameter versus Statistic, Response versus Explanatory Variable, Study versus Experiment, Bias in selecting a sample, Simple Random Sample, Stratified Sample, Voluntary Response, Control Group, Confounding and Lurking Variables, Sampling Distribution, Probability, Random Variable (discrete versus continuous), Mean, Standard Deviation, Probability Distribution, Density Curve, Normal Distributions, Proportions, Binomial Distributions, Factorials, Rules of Thumb for using Normal approximations.

Key Skills

  1. Using Table B (random digits) to select an SRS of size n from a given collection of data.
  2. Calculating means and standard deviations from data sets with values and counts (or frequencies) for each value.
  3. Calculating probabilities based on a normal distribution with a given mean and standard deviation (using normalcdf on the TI-83 or by standardizing and using the table).
  4. Calculating probabilities associated with a binomial distribution and recognizing the binomial setting.
  5. Checking the rules of thumb for using the normal approximation to sample proportion probabilities.
  6. Calculating probabilities from a table giving the distribution of a random variable, or from a graph of the density curve.

Key Facts and Formulas

  1. For samples of size n from a population with proportion p having some property, assuming
    1. n < pop size / 10,
    2. p * n and (1 - p)*n are both at least equal to 10;
    if x-bar equals the proportion of your sample which have the property, then the mean of x-bar is p; the standard deviation of x-bar is  and the distribution of x-bar is (approximately) normal.
  2. For samples of size n from any population of quantitative data with mean equal mu and standard deviation equal sigma, if x-bar denotes the average of your sample, x-bar values will have an approximately normal distribution with mean equal mu and standard deviation sigma / squareroot of n. This assumes the sample size n is relatively large (say 15 or more) but not more than the population size divided by 10. The larger the value of n, the more normal the distribution of x-bar values and the less variable the values of x-bar.
  3. All probabilities are between zero and one, and the sum of all probabilities must equal one.
  4. The mean of a random variable is the sum of each of its values times the probability of that value. If X takes on the values  x1, x2 and x3 with respective probabilities p1, p2 and p3, then mu = x1*p1 + x2*p2 + x3*p3.
  5. If X is a value from a normal distribution with mean m and standard deviation s, then the standardization of X is the value z = .

Practice Problems

3.47, 3.51, 3.59, 4.22, 4.24, 4.29, 4.35, 4.37, 4.42, 4.55 to 4.58, 4.67, 4.78, 4.84, 4.103