Final Exam Review

So this review will basically just cover the new material since Exam 3. If you want to see topics from Exam 3 and before, you can look at the three other exam reviews I have written for each exam.

However, after lab today a student said "I know everything we've learned all interconnects...but how do we keep it STRAIGHT?" It was a good question. So, the first part of this review will be an overall, comprehensive look at some things we have done this semester. You should be able to click on them to make the charts larger.

1. A list of all "tests" we have performed and why/when we perform them. (There is a document on blackboard similar to this. It tells the same information, mine is just in a different format. Use whichever one makes the most sense for you)

2. A list of all conditions for any test we have done.



3. A comprehensive list of symbols and their meanings.


Okay, on to new material.

New material mostly covers:
1. Proportions
2. Chi-Square
3. Tests of Significance on Slope (Regression)
4. (small topic) Can you tell which test to use?


1. Proportions

Proportions represent categorical variables, like survey questions. You should know:

a. How to compute proportions.

• p-hat is just "number of successes" over the total sample size, or n.

• Be able to use the test equations. BE CAREFUL on which "p" you are using- whether is is the "null p" or the "p-hat, sample p".
  
  
• Seriously though, they love to test you on that. Especially true or false. For example, "For a one-sided confidence interval estimation, we would test normality by checking np>=10 and n(1-p)>=10. You said true, right? Well it's FALSE. For confidence intervals, we check p-hat, not p. Watch out.
  
  
• Speaking of np checks, know the np checks for normality. In case you forgot, they are:
  
  

• Know how to calculate two-sample proportions, namely knowing what just "p-hat" is (the pooled proportion p-hat).
  

b. General things

• Be able to write parameters for proportions (homework is good for this).
  
  
• Know facts about the sampling distribution of p-hat (HINT: It's a lot like facts about the sampling distribution of x-bar...)
  
  
• Really anything asked in a four step process (be able to conclude, get a p-value, etc).
  

2. CHI-SQUARE

a. Computing chi-square

• Remember chi-square is just on two-way tables.
  
  
• We compute expected counts (the zorro method, row total X table total/Row total), and then the chi-square contributor for EACH cell
  
  
• We sum up all of the chi-square contributors to get the chi-square test statistic. Using the new table, which works exactly like the t-table, we get a p-value.
  
  
• Don't forget about conditions.
  
  
• Chi-square is always testing to see if there is SOME association between the variables.
  
  
• Remember the relationship between expected counts and observed counts.
  
  
• You get degrees of freedom in a different way [(r-1)*(c-1)]
  
  
• Don't talk about causation. Just don't do it. We need an experiment for causation.

3. REGRESSION / SLOPE ANALYSIS

a. Theory

• The theory of tests of significance on regression is that SLOPE determines if there is an association or not. Thus we are testing if slope is zero versus slope is not zero (greater than/ less than / not equal to).
  
  
• Be able to write/interpret a parameter in context.
  "Slope is the average change in y for every one unit increase in x"
  Change out what is in green, and you are on your merry way.
  
  
• Be sure you know how to check conditions
  

b. Calculations

• Remember, regression is really all based on the "output". Be sure you know how to read them. Then the equations become easy.
  
  
• Don't be fooled: DF=n-2.
  
  
• Conclude in a similar fashion as with every test.

c. Reminders

• Don't forget other stuff you "used to" know about regression. Namely

1. How to write best-fit equations based on the output
2. how to plug in numbers to those equations
3. r
4. r^2 (and interpretation of it)

d. Confidence Intervals versus Prediction intervals

• This is pretty simple stuff. Confidence intervals : are on means. Prediction intervals: Are on individuals
  
  
• Which one is wider, and why?

4. WHICH TEST IS IT?

As it is the end of a semester, we have gone through a whole lot of different procedures. They are going to ask you questions about "which procedure are we using?" Use the chart I gave above about all the different procedures to help you with this one.

Above all, take these slow. Eliminate one thing at a time.

Example:

"Suzy wants to test which oven is best. In oven one, she bakes ten loaves of bread and times the average time it takes for them to bake. She then puts ten loaves in oven two, and calculates the average baking time for those. She discovers, with a p-value of 0.002, that oven two cooks faster"

Answers:
a. One-sample t- test for means
b. One-sample z-test for means
c. One-sample z-test for proportions
d.Two-sample t-test for means
e. Two-sample z-test for means
f. Two-sample z-test for proportions
g. Two-sample t-confidence interval for means
h. Two-sample z-confidence interval for proportions
g. ANOVA
e. Chi-Square
f. Regression

Whoa. There are a lot of choices. Ask yourself some questions.
1. Is this for means or proportions? She is calculating the average bake time. Means.
2. Is this z or t? No mention of sigma. T-test.
3. Is this a confidence interval or test? It mentions a p-value, so test.
4. Is this one-sample, two-sample or matched pairs? There are two ovens, so two different data samples collected. This is two-sample.

The correct answer is (d).

You'll most likely never actually have to go through all of those questions, but they are good types of questions to ask to narrow things down.


For help on other exam material, see my other reviews posted.

GOOD LUCK GUYS. YOU'LL DO GREAT.

Have a great life :)
-Hillary