1. AP Statistics
Course Review

2. Exploring Data Variables can be categorical or quantitative
Discrete or continuous
For categorical data, we use bar charts
Numerical data can be displayed using a dotplot, stemplot, box-and-whisker plot, histogram or cumulative frequency plot
Remember histograms have no spaces (unless a category has none)
Must include key with stemplot
Always label axes and make sure you read the axes when interpreting a graph.

3. Commenting on a graph Shape: symmetric, skewed, unimodal, uniform
Center: Mean and median
Spread: Range, standard deviation, Iqr, gaps, outliers (1.5x iqr) added to quartile

4. Effect of changing units
Changing units will change measures of center and spread by the same ratio as the multiplier.
Adding or subtracting the same constant will change measures of center in a similar manner but will not change measures of spread.
Trial Run 1

5. Scatterplots Bivariate, explanatory, response
Correlation coefficient (r) -1 to 1
R does not change when you switch x and y, nor will it change when you multiply or add
Only measures strength of linear relationship
Affected by outliers
Lurking variables
Danger of extrapolation

6. Coefficient of determination (r2) Residuals (observed – predicted)
Influential points
Transformations
Trial run

7. Sampling Census, survey, experiment, observational study
Parameter (population) statistic (sample)
Convenience, SRS, stratified, cluster, systematic
Bias: undercoverage, nonresponse, response
Placebo, blind, randomization, replication, confounding variable

8. Experimental designs: completely randomized, blocks, matched pairs
Trial run

9. Probability
Law of large numbers: long-term relative frequency gets closer to true freq. as # trials increases
Disjoint (mutually exclusive): cannot occur simultaneously
Mand and ort
Conditional probability:
Independence: knowing one has occurred doesn’t change chance of the other

10. Probability distributions
Matches all possible values of variable with probability of it happening
All probabilities must be between 0 and 1
Total of probabilities must be 1
Mean:
Variance

11. Binomial Random Variables
Fixed number of trials, success or failure
P remains constant each trial
Each trial is independent
(nCr) pr (1-p)n-r
Mean: np
Variance: np(1-p)

12. Geometric Random Variable
Success or failure
P constant, each trial independent
How many times until ….
Probability k trials occur before …
p (1-p)k-1
Trial run

13. Combining Variables Mean (x+y) = mean (x) + mean (y)
If independent: variance (x+y)= var(x)+var(y)

14. Normal distributions Z-score
Standardize endpoints, find area under curve
Trial run

15. Sampling distributions
All possible random samples are taken and used to create a sampling distribution of the sample mean
Standard dev. :
Central Limit Theorem: as the size of an SRS increases, the shape of the sampling dist. tends toward normal

16. Hypothesis Testing Sample Proportion Ho: Ha: Test Statistic Pvalue
Assumptions: p is from a random sample
Sample size is large (np>10 and n(1-p)>10)
Sample no more than 10% of population

17. Sample Mean Ho: Ha: Test Statistic P value
Assumptions: from a random sample
Sample size is large (>30) or population distribution is approximately normal

18. Hypothesis Testing Difference in 2 sample proportions: Ho: Ha:
Test statistic:
P value
Assumptions: independently chosen random samples or treatments were assigned at random to individuals
Both sample sizes are large (np>10, n(1-p)>10 works for both of them

19. Hypothesis Testing Difference in two sample means Ho: Ha:
Test Statistic
P value
Assumptions: 2 sample are independently selected random samples
Sample size large (>30) or population distributions are approximately normal

20. Hypothesis Testing Paired t test comparing 2 population means
Ho: µd = hypothesized value
Ha: µd < > ≠ hypothesized value
Test statistic:
Pvalue:
Assumptions: Samples are paired
Random samples from a pop. Of differences
Sample size is large (>30) or population distribution of differences is about normal

21. Hypothesis Testing Chi-Square GOF Ho: Ha: Test Statistic P value
Assumptions: based on random sample
Sample size is large – every expected cell count at least 5
Degrees of freedom?

22. Hypothesis Testing
Chi-Square Test of Homogeneity or Independence (2 way table)
Ho: There is no relationship between __and _
Ha: Ho not true
Test Statistic:
P value
Assumptions: independently chosen random samples or random assignation to groups
All expected cell counts are at least 5
Degrees of freedom?

23. Hypothesis Testing (last one!!)
Chi-square test for slope
Ho:
Ha:
Test statistic:
P value
Assumptions: dist. of e has mean value=0, std. dev. of e does not depend on x, dist. of e is normal, random dev. of e are independent of each other
Degrees of freedom: n-2

24. Confidence Intervals Statistic ± margin of error(also called bound)
Margin of error is combination of 2 numbers:
(Critical value ) (standard error)