STAT 515 Honors -- EXAM 2 REVIEW SHEET 


I. Continuous Probability Distributions
 A.  Probability Density Functions
   1. Properties of a Density Function
   2. Probabilities for Continuous Random Variables
     a.  Probability a r.v. falls within a certain INTERVAL
     b.  Area under the density curve
 B.  Uniform Distribution
   1. Density Function for a Uniform r.v.
   2. Mean of a Uniform r.v.
   3. Std. deviation of a Uniform r.v.
   4. Probability a Uniform r.v. falls in a certain interval
 C.  Normal Distribution
   1. Role of mu and sigma in the normal distribution
   2. The Standard Normal and its Characteristics
   3. Finding Probabilities Involving Standard Normal Random Variables
     a.  Using Table IV to find areas under standard normal curve
     b.  Finding z-values that correspond to specified areas/probabilities
   4. Standardizing Normal Random Variables
     a. Finding Probabilities Involving any Normal Random Variable
     b. "Unstandardizing" z-values 
 D.  Normal Approximation to the Binomial
   1.  Why can we use this approximation?
   2.  When is it appropriate?  (Rule of Thumb)
   3.  Using the continuity correction

II. Sample Variability and Sampling Distributions
 A.  Statistics and Parameters
   1.  Examples of each
   2.  What is the difference between a statistic and a parameter?
 B. Definition of a Sampling Distribution
   1. Estimation of a Parameter
     a.  Point Estimation
     b.  Unbiased statistic
     c.  Standard Error of a Statistic  
   2. Pattern of Variability of the Sample Mean Across Repeated Samples
   3. Mean of Sampling Distn. of X-bar
   4. Std. Deviation (Std. Error) of Sampling Distn. of X-bar
   5. Shape of Sampling Distn. of X-bar
     a.  When original data are normally distributed?  When data are not normal?
     b.  Central Limit Theorem (CLT)
     c.  When does the CLT apply?
 C.  Using the Sampling Distribution of the Sample Mean
   1.  Using Normal Distribution Techniques to Find Probabilities involving X-bar
 D. Other Sampling Distributions
   1. t-distribution
   2. Chi-square distribution
   3. F-distribution
   4. What are the shapes of these distributions?
   5. What do "degrees of freedom" signify for these distributions?
   6. Reading t, chi-square, and F tables in textbook

III.  Confidence Intervals
 A. Precise Interpretation of a Confidence Interval
   1.  What does, for example, "95 percent confidence" mean exactly?
 B. Relationship among confidence level, sample size, and width of the CI
 C. Small-sample Confidence Intervals about a Mean (when sigma unknown)
   1. Sampling distribution of "t-statistic" (t distribution)
   2. How is t distribution different from standard normal?
   3. Reading Table VI to get critical t values
   4. Formula for CI for mu
 D. Confidence Intervals about a Proportion
   1. Definition of Sample proportion (p-hat)
   2. Sampling Distribution of p-hat
   3. Classical CI for p
   4. When can we use this formula? (rules of thumb)
 E. Other Confidence Intervals
   1. Confidence interval for the variance sigma^2 (and for sigma)
   2. Confidence interval for the ratio of two variances
 F. Sample Size Determination
   1. Sample size determination for CI about mu
   2. Sample size determination for CI about p

IV. Hypothesis Tests
 A.  Purpose of Hypothesis Testing
   1. Null and alternative hypotheses
     a.  Which one is "assumed" to be true before the test?
     b.  Which one are we "trying to prove" (seeking evidence for)?
   2. Type I error
   3. Significance level (alpha) for a hypothesis test
   4. How do we decide whether to reject H_0 (whether result is "significant")?
 B.  One-sample t-test
   1. Test statistic t
     a. What distribution does t have if H_0 is true? (degrees of freedom?)
   2. When do we reject H_0?
     a. One-tailed alternative (>)
     b. One-tailed alternative (<)
     c. Two-tailed alternative (not equal)
     d. Reading Table VI
   3. Stating conclusions in terms of the variables in the problem
   4. Assumptions and Robustness of the t procedures
     a.  When can we safely use the t procedures?
 C.  Hypothesis Test About a Proportion
   1. Test Statistic z
     a. What distribution does z have if H_0 is true?
   2. Determining rejection region (for each type of alternative)
   3. Stating conclusions in terms of the variables in the problem 
 D.  P-values
   1. Precise definition of P-value
   2. What does p-value tell us about the evidence against H_0?
 E.  The relationship between Confidence Intervals and Two-sided Hypothesis Tests
 F.  Power of a Hypothesis Test
   1. Type I and Type II errors
   2. Definition of Power
   3. Calculating the power of a test about mu (with sigma known)
   4. Calculating the power of a test about p