Final Exam Study Guide - Outline

Final Exam Study Guide
There's a lot of material to review for our final exam. In order to study for the final, I'm going through all the chapters that will be covered (6, 7, 8, 9 and 12) and pulling out the important points from each one. I've basically written them up as "learning objectives" for each chapter. Also since we didn't cover every section of every chapter, I've listed the sections that we did cover.

Here's my outline as it stands so far:

Chapter 6 - The Normal Distribution
6.1
Understand the concept of a continuous probability distribution and the difference between continuous and discrete probability distributions.

6.2
Understand the normal and standard normal distributions.
Calculate the z score for any given X.
Read the standard normal distribution table and answer questions of the form:
P(X<a)
P(X>a)
P(a<X<b)

6.3
Use the normal probability plot to evaluate normality of data.

Chapter 7 - Sampling Distributions

7.1
Understand the concept of a sampling distribution.

7.2
Calculate z-scores for xbar using the standard error of the mean: σ/√n
Understand the Central Limit Theorem.

Chapter 8 - Confidence Intervals

8.1
Construct a confidence interval for the population mean, given a sample mean, population standard deviation, sample size and level of confidence.
Know that a high level of confidence requires a wider confidence interval.

8.2
Construct a confidence interval for the population mean, given the sample mean, sample standard deviation, sample size and level of confidence.
Know that for the t statistic, the degrees of freedom is n-1.
Read the t-table to find the critical value for a given level of confidence and degrees of freedom.

8.4
Calculate the sample size required for a given margin of error and level of confidence.
Know that a smaller margin of error requires a larger sample size.
Know that a higher level of confidence requires a larger sample size.

Chapter 9 – Hypothesis Testing

9.1
Understand the concept of the null and alternative hypotheses.
Construct null and alternative hypotheses based on a description of the test.
Understand the concepts of rejection and non-rejection regions.
Understand the level of significance, alpha, of a hypothesis test.

9.2
Know the difference between a one-tailed and two-tailed hypothesis test.
Calculate critical values for the rejection and non-rejection regions for both one-tailed and two-tailed tests.
Calculate the z test statistic and compare to critical values to make a decision whether or not to reject the null hypothesis.
Calculate the p-value and compare to the level of significance to make a decision whether or not to reject the null hypothesis.

9.3
Create null and alternative hypotheses for one-tailed testing.

9.4
Use the t test statistic to conduct one and two-tailed hypothesis tests when σ is not known.

Chapter 12 - Simple Linear Regression

12.1
Understand the basic concepts of independent and dependent variables, intercept and slope.
Understand the concept of simple linear regression.
Regression: modeling a relationship between variables with a curve
Linear Regression: the curve in the relationship is a straight line (not some sort of arc)
Simple Linear Regression: only consider one independent variable as the predictor of the dependent variable
Understand the simple linear regression model formula: Y_i = β₀ + β₁X_i + ε_i

12.2
Understand the method of least squares.
Apply the computation formulas of the least squares method to compute the Y intercept b₀ and the slope b₁.
Know how to read and interpret partial computer output (Minitab) and develop the regression line based on it.

12.3
Understand the sum of squares terms SST, SSR and SSE for the measures of variation in regression.
Calculate any of the sum of squares terms, given the other two.
Understand the coefficient of determination, r².
Calculate r² given any two sum of square terms.
Know how to read and interpret partial computer output (Minitab) and calculate sum of squares terms and r² based on it.
Understand the standard error of the estimate and calculate it, given SSE or SST and SSR.

12.4
Know the four assumptions necessary to use the method of least squares in simple linear regression.

12.5
Know how to use residual analysis to validate the four assumptions.

12.6
Understand the Durbin-Watson statistic.
Know how to interpret the Durbin-Watson statistic to detect autocorrelation.

12.7
Calculate the standard error of the slope, S_b1.
Calculate the t test statistic for the slope and determine whether there is a significant linear relationship.
Know that when comparing the t test statistic for the slope to the critical t value, you use n-2 degrees of freedom.
Construct a confidence interval for the slope.

12.8
Construct a prediction interval for an individual response Y.
Construct a confidence interval for the mean of Y.
(This is as far as I got so far. More to come!)